New Strat: Between Nights 5 and 6, exit to the main menu once the elevator floods the hotel and reenter the game. This saves a couple of seconds over waiting for the natural screen transition.

Other tips I have found:

Candles: Candles despawn the Tortured Soul which isn't an issue per se. However, if you light a candle between two and three minutes or within seconds of finding the artifact on Nights 3-7, it will keep Mary from spawning until your candle burns out. Night 2 is more forgiving where Mary spawns a little after 3 minutes. Keep in mind Fire Babies move faster when a candle is lit.

Unintinded Luck: Obviously this game has a lot of luck, but there is unintended luck as well. Good luck happens on Nights 0, 4 and 5, as far as I can tell. The elevator will already be activated and only will require that you find the exit (unless doing 100%). I am still trying to find a way to get this more consistent. Bad luck happens when you fall through floor into the endless void. I believe this has to do with memory inputs from the game's side.

Asmodeus: On Night 6, he will spawn between 8 and 9 minutes. He will not spawn if you have found every important piece. On Night 7, he will spawn between 6 and 8 minutes. You can flicker your light to see where he is. Otherwise consider your run over.

Elevator Switch + Mary: For whatever reason, if you activate the elevator, it lowers the time Mary is active on the map while your character is breathing.