It took a while, but I did beat all the levels. The third one was the most difficult by far, but I felt pretty clever when I figured it out.
While the idea is very cool, the game itself is a bit unintuitive, and I think a tutorial, or at least a few more easy levels before the level 3 gauntlet would have been nice.
Overall, very nice game! Very clever. I enjoy these kinds of clever games, even though they can be a bit janky. But hey, that's what game jams are for!