I really like what you've got going here. The precision platforming without a focus on enemies and giant saws everywhere is a nice change of pace, and the movement is completely different from anything else out there. The level designs seem a little long for what they ask of the player, especially given the lack of checkpoints, but the designs themselves are great. Keep at it.
Also, I was unable to enter levels, seemingly randomly, after staring the game or completing a level. Any attempt to do so would kick me back to the main menu.