Hmmm, that's difficult.
I think that one of the problems is that people don't often encounter a mechanic like this, it's pretty unique. That might be it's strength and it's curse, because since I wasn't used to it, it wasn't intuitive to play at first. I got the rhythm of the game eventually, but it took a while.
Something that might have helped me was if there was a tutorial section, where you have very simple levels displaying the basic mechanics, such as the spinning (which was very cool, congrats) and getting used to the pushing, and possibly a combination of both. At the end there might be a slightly more complex level, which would get ppl ready for the real levels.
I'm really not a game developer, so idk much at all, but it seems to me that the difficulty ramp was very sudden. Maybe if you
smoothed it out a bit, and took it tiny steps at a time, it might be easier for ppl to grasp.
EDT: I read some of your comments below, and I totally get why you'd want to make it more of a discovery thing, it was definitely very satisfying for me when I figured it out. So, idk really. I've just put my two cents out there, hope it's helpful
Thanks for the game!! :)