OH MY GOD I GOT TO THE END AND THOUGHT THERE WAS SOMETHING ON THE BOTTOM OF A TUNNEL AND DIED WHILE LISTENING TO THE SECRET THING AFTER THE BUTTON ;~;
Urgh. Yeah, you're right, checkpoints really ARE important. Even though I did it in one go, it isn't that accessible to players. But you've got that figured out already - as you have figured out a LOT of interesting scenarios that makes the idea work! I Actually think you can expand this idea in so many different ways you could actually make a fully-fledged game all around it!
However, I believe that, while the level design is already pretty great at teaching you stuff, it needs some tweaking, specially if you try and make a "flow" curve following your game's skill-to-difficulty ratio, you'll see it isn't exactly a straight line and it swerves violently up and down several parts. Not only that, I think you could do a lot of fun stuff with the fact you can't jump while on the ceiling. Suddenly a spring on the ciling is something you have to be careful, maybe! (and not just part of a challenge that starts on the ground). Also, again, I feel like there could be more situations making use of the fact you float above chasms. But honestly, execution is amazing, and I can see you're a talented and experienced dev having a lot of fun! (I swear I really REALLY wanna try beating the game again to get to the ending again. I want to see it alllll ;~;)