Love this idea! There are a lot of things you can do with this. However, I encountered a glitch where, at the bottom of the staircase, I would fall through. I wish you could teleport in the map room, though.
I experienced the same glitch. you need to fall down the center of the stairs, just so you land on the land floor before the hole. go up the stairs into the closest room. it goes nowhere, and the back wall has no collision. if you go through that wall, you end up in the room above. go down the stairs, aaaaand the floor is gone. falling in causes a eternity of falling.
great game though! I love the non-Euclidean style!