Fun idea, though I'll admit that I got stuck early -- first at the room with the "below" disk, then at the room with the "empty" disk. I felt like I understood what I was attempting to do, but then couldn't work out the mechanics to do it.
I'm generally not great at puzzle games, so I find "hint" mechanisms which can give me a clue when I get stuck pretty helpful; I don't know if it would make sense here, but something to think about.
Cool idea, even if I ended up being very bad at it!