Most of the level can be bypassed by holding right...
From the screen with all of the trinkets (Way too red), you can land safely on one of the checkpoints on the final screen by holding from the first checkpoint.
Although this can be fixed by adding vertical warps, it would just become a tedious chore; due to its single task.
All in all, not too enjoyable. Needs a bit more variation.
Concerning the puzzle, I don't think there's any way to make it work, honestly. It'd be too easy by adding retaining walls, etc.
EDIT: After testing it a couple of times, you're pretty much guaranteed to land on another checkpoint by holding down right from any checkpoint. I completed the level in three flips, from the beginning to middle, middle to end, and once more as I was on the wrong side of the platform.