Putting a timer on the end screen was a nice idea, though I don't think I'll ever be good enough to speed run it :P
The animation for changing layers is very cute, and changing the colour helps keep it very readable.
It could use some platformer conveniences, like coyote time, and not colliding with platforms from below. I would also echo what others have said about space feeling like a jump button. I kept pressing it out of habit, and falling through the floor. Enter for the switching might be less confusing.
You made a nice range of challenging levels. At times it was almost frustrating, but I think it was just on the right side of that. The "sorry" made me laugh.