The end step only begins once, this is a very specific point in the turn structure, it is not a duration. Basically, the beginning of the end step is the time when the game moves from the second main phase to the end step. Any delayed triggered abilities and objects with triggers that trigger "at the beginning of the [next/your] end step" must exist prior to this specific point in time or they don't trigger. Nothing in the game ever triggers retroactively.
Former Rules Advisor
"Everything's better with pirates." - Lodge
(The Gamers: Dorkness Rising)
"Any sufficiently analyzed magic is indistinguishable from science."
(Girl Genius - Fairy Tale Theater Break - Cinderella, end of volume 8)