Wow, this is such an ingenious puzzle game! And it fits the theme incredibly well!
The only problem I've had with it was when I would remove blocks in a non-symmetrical order, as the center point would remain in the same relative place, instead of moving to the new center of mass. (But that seems like it would be easily fixed by changing the parent's position to the new center, so it's not a big deal)
I can also see this game having a lot of potential for new puzzles, by starting out in other, more irregular, shapes and composed by different block types (bouncy and heavy blocks, that push the center of gravity closer to one side, are just two that come off the top of my head).
You could even be really ambitious and add a glue block, which would allow you to re-attach to discarded blocks (tough, that seems like a nightmare to implement :D)
(I will say that I have gotten somewhat stuck, after reaching the level from the first screenshot. I don't know if that's the end, or if I haven't figured out how to progress yet, so some guidance would be appreciated :))
All in all, this game is amazing, you two have done an outstanding job! Congrats! :D
I hope you're planning on continuing to work on this game, because I would love to play a fuller, more extended version of this game ;)