There's plenty of potential here, great idea!
The splitting mechanic was a really cool extra twist, which really expanded upon the base idea of the game, allowing the player to make much more interesting and diverse shapes so well done :D
I think the main thing that it struggles with is that the player sometimes can't really make sense of the depth until it's too late, so I made a little sketch of a potential solution:
Not entirely sure how this could translate into the game when you have a bunch of different split parts, but I think the main thing would be to highlight on the wall where the cube is currently lined up and draw sharper "Guide" lines along the side edges. if you didnt want to do the guide lines, you might even be able to get away with just having a second, identical, player mesh attached to the wall where you're going to collide, which might be an easier method.
I also think something that would take the game to the absolute NEXT LEVEL, would be to sort of extrude one side at a time, rather than scaling the whole object, which would keep the cube in place as you changed its scale. making it more predictable.
Anyway, I think you should keep running with this idea cause you can clearly get a lot of milage out of it, very clever! really good work :)