Sins of the Past does not have any triggered abilities. If you cast the card and something attempts to move it from the stack to the graveyard by any means (its own resolution, being countered by Cephalid Shrine, or being countered for lack of targets), it doesn't actually make it back to the graveyard, it goes to exile instead. If it makes any other zone change, either before you cast it or afterward, it loses its object identity, and the continuous effect created by Sins of the Past that looks at it is no longer doing so. Obviously, the card being shunted off to exile counts as "any other zone change", so one way or another the effect will end, and then if it goes back to the graveyard somehow it will be completely dissociated from any prior copies of Sins. Nothing will give you permission to cast it, and nothing will replace any future movements that take it to the graveyard, unless and until you target it with Sins yet again.
I remember Epic Experiment was tried in some old extended-deck cuts, under the premise that it's non-targeted and using a copy of it to fetch itself would be useless, but would it do anything here?
Ray of Revelation is another way that green mana can turn into enchantment targeting, in case the first "free" cast helps to build anything up.
There's nothing that targets Spirits for blue mana alone, so as to possibly drop Izzet Guildmage and free a slot. There is still Master of the Veil as a possibility, of course, but one thing I was looking at was Walker of Secret Ways. Good enough, or would we need the extra ninja to be red instead of black?
Drowner of Secrets can use Changeling Berserker and summoning-sick merfolk, as well as its own Dual Nature copy, to mill cards. Does that give it enough power for this, or possibly even too much power?
The potential breaking point that popped out at me was a Possibility Storm triggering on Precursor Golem and fetching Black Lotus as a source of mana. But nothing can target Precursor Golem short of Mark of Mutiny, so that looks safe. For that matter, nothing gets Black Lotus out of the graveyard once it pays for the initial cost of Show and Tell, so it's really safe.
Not quite. The presence of Joraga Warcaller and Conspiracy means that once you get a +1/+1 counter on Warcaller by any means, you can play Clone and not have it copy anything, and the Warcaller's pump will give Clone a positive toughness so it doesn't die right away. Then you can tap Kiki-Jiki to make a copy of Clone, and since you specifically did not commit to anything on the copy effect originally, now you get a new chance to declare a commitment for what the token Clones will be copying. Notably, you can have a Clone token enter as a copy of Kiki-Jiki, ready to tap again and target the original, and so on forever.
Wet Willie of the Damned would be perfect, except for the border color. And you thought you couldn't tempt the Pain Magnification line with any more than 2 damage.
Other than that, the search is coming up shockingly empty, and that's without even taking into account that a number of card profiles are going to be off-limits up where this card is going to have to reside (sorceries < 3, instants < 4, white or multicolored cards regardless of CMC). There are some that target only players and therefore won't get Precursor triggers (Touch of Death, Vampiric Touch), some that target only creatures and therefore won't get Night Dealings triggers (Last Kiss, Feast of Flesh), and a whole host of spells for either X damage or a fixed damage that's at least 3. There's also Searing Meditation, which can turn one lifegain event into X damage events, and that doesn't seem likely to play nice with the order of resource flow up there.
Pyromancer Ascension goes active from all the Clone Legions. Once that's in place, you can play any of your targeted graveyard-return cards such as Treasured Find or Vengeful Rebirth. It doesn't really matter what you target; Pyromancer Ascnsion will trigger on top of the spell, making copies that resolve before the original and that allow you to regrow more cards. In particular, you can duplicate the original target for one of the copies, so that the copy will return it first. When the original spell resolves, it no longer has a target, so in fact it's countered and does not resolve, meaning it does not get exiled. It sits there in the graveyard, ready for you to return it by playing another copy of the spell, and so on back and forth. That continues without limit, and the deck is lost because of it.
Measuring fastest in terms of priority passes, a Leyline-powered Mana Clash or Game of Chaos is clearly faster than anything else. If you have to be able to guarantee your win given the assumption of no interference and actually having the right cards in your starting hand, then it can be done in 4 priority passes, with Leyline into 4 ESGs powering out both Channel and Primal Surge, in a deck where those are the only two nonpermanent cards. Flip everything over to include at least 1 land, Chromatic Sphere, and Laboratory Maniac, then you win with no further passes.
If fastest is being measured in terms of fewest phases/steps elapsed, then there are a number of different solutions that all finish in the first upkeep, and obviously no way of performing meaningful actions prior to that step, so that's clearly the best you can do. From there the discussion went on to the most resilient possible setup that still finishes within that timeframe of the first upkeep, whish has no real clear answer because there a number of different foils that you want to watch out for.
It might actually be better if you drop both Pacts, and replace them with Marrow Shards + Patrician's Scorn. Marrow Shards is a dummy spell, but it serves a couple key purposes: unlike Pact of Negation, it can be played as the first spell of the game, effectively "wasting" any Chancellor of the Annex triggers on a spell where you obviously don't care if it gets countered, instead of having to run out Flash as your first spell and just plain losing to a Chancellor. Additionally, the fact that it's a white spell turns on Patrician's Scorn, allowing you to sweep away any problematic Leylines, particularly Void which would otherwise hose any Protean Hulk deck no matter how much counter backup it comes with.
The fact that you rely on Gemstone Caverns to tap for blue is unfortunate, because it leaves you completely hosed half the time against any deck that prefers to go second--and most likely, all the decks are going to want to make that choice unless they plan to set up something like Grand Abolisher.
There are a few other things that Flash can put down which don't care about a Leyline in order to be effective: Composite Golem basically turns Flash into Channel the Suns, while Treasonous Ogre can let you get RRRRRR out of it (or 1 mana less if you had to dummy out a Marrow Shards or other Phyrexian spell beforehand). Woodland Bellower is basically a watered-down Hulk that only gets a single comparatively weak creature in exchange for not having to get a death trigger, and the nonlegendary rider rules out fetching Dosan the Falling Leaf. None of those is likely to do any better, particularly when they still rely on a bare Flash resolving, and even casting Flash in the first place relies on somehow getting a blue mana.
Leyline of Anticipation, Leyline of Lifeforce, Elvish Spirit Guide, Krosan Wayfarer, Serra's Sanctum, and Grand Abolisher can be used to get an uncounterable Abolisher in the first upkeep, on the play--although it's still susceptible to an opponent who can destroy either Leyline or simply go off in response to the Wayfarer. Worse yet, the fact that this consumes 6 cards means there's not enough for any follow-up: if it could be done in 5, then being able to hide behind an Abolisher allows you to refuel even with something as blunt as Black Lotus/Timetwister.
That is quite a wasteful Hulk package, leaving plenty of things to respond to after you have to commit those life-drain triggers to the stack. It doesn't help either that Disciple's trigger is targeted, so a single Leyline of Sanctity shuts you down cold.
If you're going first, the package you want to get is Grand Abolisher + Balustrade Spy. Target yourself for a full-deck mill, and the opponent is shut out of any further responses as soon as you reveal the pair of creatures. The ultimate win condition after that is usually Laboratory Maniac, but they can't interfere with it regardless of what it is. Unless, of course, they led with Leyline of the Void which prevents any Hulk from ever triggering in the first place, so it won't matter what package you plan on getting.
Going second, your options for shutting them off aren't nearly so clear-cut. Teferi, Mage of Zhalfir exists to shut your opponent out of responses no matter whose turn it is, but that uses a whopping 5 out of your 6 mana. Traditional Hulk kills have started with Body Double + a sacrifice outlet such as Viscera Seer, and turned that into a second Hulk trigger that gets Reveillark + Death Cultist, which can still go off in the upkeep but likewise doesn't attempt to shut them out of responses wholesale.
Depending on what you mean by "fastest", an opening hand of Leyline of Anticipation, Simian Spirit Guide, Mana Clash, and 4 slots of anything can, with the luck of 42 coin flips and no responses, end the game after just 2-3 priority passes, where your Disciple of the Vault outline needs at least 48.
Your decklist is currently at 61 cards without Omniscience or Enter the Infinite. The other thing that's striking about that list is that you use 4 Mana Echoes but don't actually use any of the mana for anything except Banefire, and your Praetor's Counsels are likewise underwhelming. In fact, playing out your enchantments in the first place is the most powerful step in the entire procedure, and everything after that is just moseying along without really changing anything that's notationally meaningful.
A simple Clone or Clever Impersonator would do so much more, since you could play it without copying anything, let it die as a 0/0 creature, let Dual Nature kill off all the tokens that share a name with it (hint: there are none), then get some Clone tokens that are free to copy whatever you want, such as Dual Nature and Doubling Season--the multitude of tokens can copy several different things. Then, because you actually have a permanent card in the graveyard, Praetor's Counsel can bring it back so you can replay it and get even more Dual Nature triggers. It's a rather crude and limited way of recycling or bouncing a permanent, but even just those 5 casts of Clone would do more for the total than all the redundant cards that currently fill steps 2 and 3.
Lumberknot (and possibly also Garza Zol) spoils Ion Storm, but fortunately both of those cards are just Chrome Mox enablers, so any other green Treefolk/blue Vampire can replace them for minimal loss.
Since Psychic Battle is still there, Reality Strobe and Venser's Diffusion can squeeze an extra card (and 2 layers) into the Chaos Warp shaped hole, although Chaos Warp has to stay in the deck given its role in setup. Weed Strangle also scales slightly better than Poison Arrow. We can't go to Profane Prayers if Night Dealings is still going to be used, because that can be redirected to a player and give Night Dealings triggers for a closed loop. Another option in that slot is Wrack with Madness, which can target an Everglove Courier that's been given lifelink from Nectar Faerie and a whole bunch of +1/+1s from green Paragons--and notably, that Courier has the potential to be donated, allowing either player to gain life off the spell and rendering Phelddagrif unnecessary (but we also can't add Repercussion, and its layer of triggers, for the same reason).
[EDIT] If there's a limit to how big our own life total can get by making a lifelink creature fight itself with Wrack with Madness, then clearly there's a limit to how big the opponent's life total can get using Donate and the same. Then that itself can be the limiting factor of the Night Dealings step, rather than having to donate a Soul Echo to the opponent or anything like that: Chandra's Ignition is capable of being recurred in the same ways as Wrack with Madness is, and can be used to gain large amounts of life just like Wrack with Madness, but since it says "target creature you control" instead of "target creature", it can't give the opponent any life. Furthermore, since the deck currently has no creatures that are capable of surviving at 0 power (unless we somehow forgo a Gideon emblem, attack with Karn, and let it get blocked by a donated creature...and that's assuming we even have enough setup tools to get to that position), each resolution of Chandra's Ignition is guaranteed to deal damage to the opponent, which means before we can allow that copy to resolve, we have to raise the opponent's life total high enough to survive it.
Ideally it should hit them for the full effect of their life total minus 1, to get the most out of the fixed number of Precursor copies we have, but that might be problematic. Chandra's Ignition causes the creature to indiscriminately hit all creatures on both sides, and we don't want to lose anything like Bloodbond March that serves to store our current level of progress. For Bloodbond March itself, it's less of a problem, because it receives pumps from both color of Paragons. Still, any Elf or Faerie is guaranteed to be at least as big as the Paragons that are pumping that color up, making that pump go away. Even more troubling, we really don't want to lose the Leyline of Anticipation, and yet we have no way at all to pump it beyond 5 toughness (other than getting more Gideon emblems, a process that can only be done once per round of Chaos Warp, after the stack clears, and which will pump everything else including the intended damage-dealer at the same rate). This is unfortunate for a card with as helpful a profile as Chandra's Ignition. Fiery Gambit, a card that works for us completely unlike any other application of the card in all of Magic, occupies a similar profile except that the Magical Christmasland Jackpot, "draw nine cards", is ultimately fatal.
Other options for a profile of sorcery 3+ or instant 4+, can target a creature, can deal damage to a player, the amount of damage is determined at resolution time, amount of damage isn't bound by a nonexistent or hard-capped resource (such as the number of lands, or the converted mana cost of a single card)...hmm, actually instant 3+ is safe as long as it doesn't gain life or have the creature deal the damage. That means Massive Raid is potentially a go, but we have no sacrifice outlets in the traditional sense and all our low-level board development is based on iterating the successor function, so getting the opponent's life total high enough to exceed our own creature may require tearing down a large chunk of the board, using things like other Massive Raid or Wrack with Madness copies. Cinder Cloud is another theoretically workable option, if a bit unwieldy; the only white creature in the deck that can be pumped up as the spell allows is Grassland Crusader. Finally, the only other option I found is Roar of the Crowd, which seems ideal for cherry-picking a creature type whose fractional representation is on par with the opponent's life total.
So now we just need a way to plug opponent's life total into card draws, but have about zero cards to do it in.
One thing to keep in mind is that Monk Idealist has a triggered ability, and a targeted triggered ability at that. By the time it's possible to do anything "in response to" the triggers, you already had to place the triggers on the stack, and choose targets for them. Let's say you get a batch of 128 tokens (in reality, all your batches will be much bigger of course). That's 128 triggers for which you have to choose a target before any of them can resolve, and the target must be an enchantment card that is in your graveyard right at that very moment. If all of them target the same Copy Enchantment, then the first one resolves and returns it to your hand. No matter what you do with that card thereafter, even if it returns to the graveyard before the next ability's turn, that's not good enough: the other triggers have all lost track of their target, and end up being completely wasted. The Monk Idealist step is thus almost a non-step.
Suppose you replaced Monk Idealist with Drake Familiar. That returns an enchantment from the battlefield instead of from the graveyard, so you don't get to sacrifice it, but more relevantly it does no in a non-targeted way. You don't determine which enchantment, if any, that you want to bounce until resolution time, so every single copy that you get out of a batch of tokens will still be effective.
In fact, the deck already effectively has 5 Dual Natures, because Copy Enchantment can copy them for the interleave. Of course, it still has its own copy-nothing interleave possible, and that's useful for a couple different things.
Mana Reflection is a clear upgrade over Mana Flare, since each copy doubles the mana instead of just adding 1. The power of Mana Reflection to add an arrow to the expression isn't realized here, though, because that would require a repeatable mechanism that costs only mana (rather than mana and a card) in order to produce more tokens, and in particular more Mana Reflection tokens--but with Kiki-Jiki and Earthcraft here, it's difficult to imagine how such a mechanism could ever be safe.
For best effect, Praetor's Counsel should be played with full replicate, and given the amount of mana at play here (regardless of the choice of Mana Flare/Reflection), that does add an arrow, and then three more iterations. The final result then looks to be 2^^^^^^6 (2->6->6) rather than 2^^^^^26 (2->26->5). Additionally, once the stack is down to the last Praetor's Counsel, he should sacrifice a bunch of stuff to put regeneration shields on a Boros Reckoner in advance: everything except Boros Reckoner, Dual Nature, and Doubling Season (including the Copy Enchantments that don't share a name with any tokens) is better off being sacrificed so it can be returned and replayed. Too bad he doesn't have a Leyline or Orrery to give things flash, or this could be done in front of every copy of Praetor's Counsel, not just the last. The extra regeneration shields are of course not enough to make a notational difference either way.
I remember Epic Experiment was tried in some old extended-deck cuts, under the premise that it's non-targeted and using a copy of it to fetch itself would be useless, but would it do anything here?
There's nothing that targets Spirits for blue mana alone, so as to possibly drop Izzet Guildmage and free a slot. There is still Master of the Veil as a possibility, of course, but one thing I was looking at was Walker of Secret Ways. Good enough, or would we need the extra ninja to be red instead of black?
Other than that, the search is coming up shockingly empty, and that's without even taking into account that a number of card profiles are going to be off-limits up where this card is going to have to reside (sorceries < 3, instants < 4, white or multicolored cards regardless of CMC). There are some that target only players and therefore won't get Precursor triggers (Touch of Death, Vampiric Touch), some that target only creatures and therefore won't get Night Dealings triggers (Last Kiss, Feast of Flesh), and a whole host of spells for either X damage or a fixed damage that's at least 3. There's also Searing Meditation, which can turn one lifegain event into X damage events, and that doesn't seem likely to play nice with the order of resource flow up there.
If fastest is being measured in terms of fewest phases/steps elapsed, then there are a number of different solutions that all finish in the first upkeep, and obviously no way of performing meaningful actions prior to that step, so that's clearly the best you can do. From there the discussion went on to the most resilient possible setup that still finishes within that timeframe of the first upkeep, whish has no real clear answer because there a number of different foils that you want to watch out for.
The fact that you rely on Gemstone Caverns to tap for blue is unfortunate, because it leaves you completely hosed half the time against any deck that prefers to go second--and most likely, all the decks are going to want to make that choice unless they plan to set up something like Grand Abolisher.
There are a few other things that Flash can put down which don't care about a Leyline in order to be effective: Composite Golem basically turns Flash into Channel the Suns, while Treasonous Ogre can let you get RRRRRR out of it (or 1 mana less if you had to dummy out a Marrow Shards or other Phyrexian spell beforehand). Woodland Bellower is basically a watered-down Hulk that only gets a single comparatively weak creature in exchange for not having to get a death trigger, and the nonlegendary rider rules out fetching Dosan the Falling Leaf. None of those is likely to do any better, particularly when they still rely on a bare Flash resolving, and even casting Flash in the first place relies on somehow getting a blue mana.
Leyline of Anticipation, Leyline of Lifeforce, Elvish Spirit Guide, Krosan Wayfarer, Serra's Sanctum, and Grand Abolisher can be used to get an uncounterable Abolisher in the first upkeep, on the play--although it's still susceptible to an opponent who can destroy either Leyline or simply go off in response to the Wayfarer. Worse yet, the fact that this consumes 6 cards means there's not enough for any follow-up: if it could be done in 5, then being able to hide behind an Abolisher allows you to refuel even with something as blunt as Black Lotus/Timetwister.
If you're going first, the package you want to get is Grand Abolisher + Balustrade Spy. Target yourself for a full-deck mill, and the opponent is shut out of any further responses as soon as you reveal the pair of creatures. The ultimate win condition after that is usually Laboratory Maniac, but they can't interfere with it regardless of what it is. Unless, of course, they led with Leyline of the Void which prevents any Hulk from ever triggering in the first place, so it won't matter what package you plan on getting.
Going second, your options for shutting them off aren't nearly so clear-cut. Teferi, Mage of Zhalfir exists to shut your opponent out of responses no matter whose turn it is, but that uses a whopping 5 out of your 6 mana. Traditional Hulk kills have started with Body Double + a sacrifice outlet such as Viscera Seer, and turned that into a second Hulk trigger that gets Reveillark + Death Cultist, which can still go off in the upkeep but likewise doesn't attempt to shut them out of responses wholesale.
Depending on what you mean by "fastest", an opening hand of Leyline of Anticipation, Simian Spirit Guide, Mana Clash, and 4 slots of anything can, with the luck of 42 coin flips and no responses, end the game after just 2-3 priority passes, where your Disciple of the Vault outline needs at least 48.
A simple Clone or Clever Impersonator would do so much more, since you could play it without copying anything, let it die as a 0/0 creature, let Dual Nature kill off all the tokens that share a name with it (hint: there are none), then get some Clone tokens that are free to copy whatever you want, such as Dual Nature and Doubling Season--the multitude of tokens can copy several different things. Then, because you actually have a permanent card in the graveyard, Praetor's Counsel can bring it back so you can replay it and get even more Dual Nature triggers. It's a rather crude and limited way of recycling or bouncing a permanent, but even just those 5 casts of Clone would do more for the total than all the redundant cards that currently fill steps 2 and 3.
Since Psychic Battle is still there, Reality Strobe and Venser's Diffusion can squeeze an extra card (and 2 layers) into the Chaos Warp shaped hole, although Chaos Warp has to stay in the deck given its role in setup. Weed Strangle also scales slightly better than Poison Arrow. We can't go to Profane Prayers if Night Dealings is still going to be used, because that can be redirected to a player and give Night Dealings triggers for a closed loop. Another option in that slot is Wrack with Madness, which can target an Everglove Courier that's been given lifelink from Nectar Faerie and a whole bunch of +1/+1s from green Paragons--and notably, that Courier has the potential to be donated, allowing either player to gain life off the spell and rendering Phelddagrif unnecessary (but we also can't add Repercussion, and its layer of triggers, for the same reason).
[EDIT] If there's a limit to how big our own life total can get by making a lifelink creature fight itself with Wrack with Madness, then clearly there's a limit to how big the opponent's life total can get using Donate and the same. Then that itself can be the limiting factor of the Night Dealings step, rather than having to donate a Soul Echo to the opponent or anything like that: Chandra's Ignition is capable of being recurred in the same ways as Wrack with Madness is, and can be used to gain large amounts of life just like Wrack with Madness, but since it says "target creature you control" instead of "target creature", it can't give the opponent any life. Furthermore, since the deck currently has no creatures that are capable of surviving at 0 power (unless we somehow forgo a Gideon emblem, attack with Karn, and let it get blocked by a donated creature...and that's assuming we even have enough setup tools to get to that position), each resolution of Chandra's Ignition is guaranteed to deal damage to the opponent, which means before we can allow that copy to resolve, we have to raise the opponent's life total high enough to survive it.
Ideally it should hit them for the full effect of their life total minus 1, to get the most out of the fixed number of Precursor copies we have, but that might be problematic. Chandra's Ignition causes the creature to indiscriminately hit all creatures on both sides, and we don't want to lose anything like Bloodbond March that serves to store our current level of progress. For Bloodbond March itself, it's less of a problem, because it receives pumps from both color of Paragons. Still, any Elf or Faerie is guaranteed to be at least as big as the Paragons that are pumping that color up, making that pump go away. Even more troubling, we really don't want to lose the Leyline of Anticipation, and yet we have no way at all to pump it beyond 5 toughness (other than getting more Gideon emblems, a process that can only be done once per round of Chaos Warp, after the stack clears, and which will pump everything else including the intended damage-dealer at the same rate). This is unfortunate for a card with as helpful a profile as Chandra's Ignition. Fiery Gambit, a card that works for us completely unlike any other application of the card in all of Magic, occupies a similar profile except that the Magical Christmasland Jackpot, "draw nine cards", is ultimately fatal.
Other options for a profile of sorcery 3+ or instant 4+, can target a creature, can deal damage to a player, the amount of damage is determined at resolution time, amount of damage isn't bound by a nonexistent or hard-capped resource (such as the number of lands, or the converted mana cost of a single card)...hmm, actually instant 3+ is safe as long as it doesn't gain life or have the creature deal the damage. That means Massive Raid is potentially a go, but we have no sacrifice outlets in the traditional sense and all our low-level board development is based on iterating the successor function, so getting the opponent's life total high enough to exceed our own creature may require tearing down a large chunk of the board, using things like other Massive Raid or Wrack with Madness copies. Cinder Cloud is another theoretically workable option, if a bit unwieldy; the only white creature in the deck that can be pumped up as the spell allows is Grassland Crusader. Finally, the only other option I found is Roar of the Crowd, which seems ideal for cherry-picking a creature type whose fractional representation is on par with the opponent's life total.
So now we just need a way to plug opponent's life total into card draws, but have about zero cards to do it in.
Suppose you replaced Monk Idealist with Drake Familiar. That returns an enchantment from the battlefield instead of from the graveyard, so you don't get to sacrifice it, but more relevantly it does no in a non-targeted way. You don't determine which enchantment, if any, that you want to bounce until resolution time, so every single copy that you get out of a batch of tokens will still be effective.
Mana Reflection is a clear upgrade over Mana Flare, since each copy doubles the mana instead of just adding 1. The power of Mana Reflection to add an arrow to the expression isn't realized here, though, because that would require a repeatable mechanism that costs only mana (rather than mana and a card) in order to produce more tokens, and in particular more Mana Reflection tokens--but with Kiki-Jiki and Earthcraft here, it's difficult to imagine how such a mechanism could ever be safe.
For best effect, Praetor's Counsel should be played with full replicate, and given the amount of mana at play here (regardless of the choice of Mana Flare/Reflection), that does add an arrow, and then three more iterations. The final result then looks to be 2^^^^^^6 (2->6->6) rather than 2^^^^^26 (2->26->5). Additionally, once the stack is down to the last Praetor's Counsel, he should sacrifice a bunch of stuff to put regeneration shields on a Boros Reckoner in advance: everything except Boros Reckoner, Dual Nature, and Doubling Season (including the Copy Enchantments that don't share a name with any tokens) is better off being sacrificed so it can be returned and replayed. Too bad he doesn't have a Leyline or Orrery to give things flash, or this could be done in front of every copy of Praetor's Counsel, not just the last. The extra regeneration shields are of course not enough to make a notational difference either way.