There's also the ability to undo steps btw
Than you can't be stuck in a corner and I would suggest to only have, in addition to undo, the press R to restart a room.
The problems you have with the lack of purpose and not liking diamonds should hopefully be changed when we finish the story of the game.
<The diamonds> ... are supposed to be the main reason you are solving the puzzles. They serve a story purpose as well as a puzzle purpose at times.
Obviously I haven't played the game and I'm only trying to explain my though. It sounds like the game would not be changed if you removed the diamonds. I don't have all the "pieces" but if they only serve as motivator to solve puzzle, story element or to unlock/buy something they are not part of the gameplay and a better alternative could be found (in my opinion). Progressing in the game is a reward in itself and a better motivation to solve puzzle for me.
For the title graphics: the name is ok with me, but the graphics are not tight together, and they are three different colors. It makes me think (interpret) that there are three games, or three different part in the game, clearly separated.
Visually the fact that they look like three different squares put next to each other doesn't look interesting or interestingly balanced to me.