Cute game!
I like the visual presentation a lot, the minimalistic look really works when you keep it clean. I think it works very well for this game, and some squash and stretch + other small animation additions can go a long way to give it a little bit more juice. Just a simple animation for when you get the block into the final spot would go a long way for the satisfaction of winning.
The spin on the general move count idea is cool, since you don't truly have to plan out every single step, but do need to be aware of where you will respawn and make use of it. Although, I don't think too many levels used this to its full strength, and for most of them respawning didn't make a huge difference in solving. With a mechanic like this, there is a lot of room to explore more interesting ideas. Like maybe having different spots you will spawn from, either in a turn order or needing to stand over them to activate them.
Originally, I also read the tagline for this game as once you run out of turns, your cube will stay there frozen, but you get to come back as another one. And I think there is also maybe some puzzle potential with that, in creating walls with your past selves to get the block to turn.
Having a quick reset is nice, but for games like this it is especially nice to have a simple 1 turn undo. Since a single misplaced push can usually end an entire attempt. And by giving this to players, you can also make harder levels, since the players shouldn't be worried about experimenting with ideas since they know it'll be easily undone.
Nice work!