Nice little game.
The only technical issue I see is with the layer switching.
The staircase right after the begining, for exemple, always place the character object on the layer of the staircase upon reaching it.
This makes it so if the left arrow is pressed, the player will always go up and not back the way it came. That is unless the player goes up a few stairs, go back down and then go left.
Instead of an instant switch on entering a trigger, an UP/DOWN input would solve the issue gracefully while adding just a bit of depth regarding the interaction of the player with the game world.