This feels like a fantastic puzzle game, but I am far too smooth brain for this. I only got to level three, and I can't see any path to a solution. The mechanics are simple enough to grasp from the first level, but I feel like I was thrown into the deep end with these levels.
If you do choose to improve this game after the jam, I would recommend inserting some intermediate levels to help smooth out the difficulty curve.
All in all, excellent work!