Awesome game, great concept especially. Would definitely play a fully worked out version of this!
Here's a couple of things I experienced to maybe keep in mind.
Firstly, the cube was a bit unwieldy, I lost track of where I was all the time.
Secondly, not all puzzles felt as deliberate. I feel like I 'cheated' most of the puzzles by "cubing the egg". This was also because the possibility space was so huge, right from the start. It might be hard to force an interesting solution if you don't limit the player in some way (especially at the beginning). It feels a bit cheap if the solution was only one or two moves that you just hadn't seen.
The second to last puzzles was a great example of forcing the player to stay in the middle lane, which made for some nice a-ha moments.
Lastly, and really nitpicky, it also feels kinda weird that the egg doesn't respect gravity.
Sorry to sound so negative, I'm actually really positive about it and I'm glad I played this!