Does drawing a card in the draw phase use the stack, and related Laboratory Maniac shenanigans
I wrote the question, and in the course of writing the question, I figured out the answer.  So, here's my stab at the answer.

S1)  Drawing during the Draw Phase does not use the stack, so you cannot win in this situation.  You must kill the Maniac before the draw phase, but with no maniac on the table, Abundance will keep them from losing the game.

This is covered in rule 504:


  
  Draw Step
  
  
  504.1. First, the active player draws a card. This turn-based action doesn’t use the stack.


S2) Abundance is a replacement effect, so the decision about whether or not to use the abundance is made at the time of the draw.  Thus, if you kill the Maniac at anytime before Nin's draw occurs, your opponent can just chose to use abundance, to avoid losing the game.