So first thing: I loved the core mechanic. Reminded me a lot from that one segment in Braid. After figuring out and completing each level I felt smart! To me, this is the objective of any puzzle game, and yours achieve that.
However, by the retrying nature of the mechanic, plus the solving problems difficulty, I would suggest you to remove any friction with movement and objects placement. Unless you wanted to explore this in later levels.
Also, I really liked the eerie aesthetics of the game, with all those noise effects. My only suggestion would be to lower the volume and add some variations to the jump / landing sounds.