Wow, this game has got a lot of detail! And a pretty unique mechanic too, I've only seen one game with stacking dolls before (Stacking, 2011) but that was more adventurey than pure puzzle. I'm a fan of the design that goes into puzzle games so this one intrigued me quite a bit.
I ended up feeling quite split, because the later levels turned into more trial and error than anything. Since I can't see the whole level at once, I would try to step on the first buttons I could see, and if they weren't correct then try again with a new set of buttons. There was no way to change my previous positions without restarting and I'm not sure if this is a good thing or not.
On the one hand, you have to factor it into your solutions, you can't move once you've split off. On the other, I can think of so many more puzzle opportunities if you could rejoin with a previous doll to move it. You could open up a gate, move a doll through, leave one behind on the button, and then join back with the original and lock the previous doll on the other side of the gate.
You could have smaller levels that are still more difficult than the existing large ones, and the player can undo any decision at any time by tracing their steps backwards, rather than restarting entirely. Right now the difficulty seems to come from obfuscation, you can't see everything at once so it's harder. I think the real strength in your idea is about pressing buttons in the right order, and implementing the size of the dolls into the puzzle too (need a large doll to press a big button, a small doll to fit through a small gap).
Anyway, sorry for the ramble! Just some thoughts on how your clever game idea could be extended to have a bunch of new things to think about! Thanks for putting in all the work to make this!