Fun idea! I have to say though, what the game considers heart-shaped and what I consider heart-shaped don't seem to be the same thing. At first when I made something actually heart-shaped, the game simply showed a "6" and did nothing else. Then I removed all the pieces and placed only the 90° circles in the top corners. Nothing else. The game considered that a perfect heart!
I like the concept. I like the fact that placing the piece also rotates it, and clicking any overlapping shapes rotates them all, so you have to think about the current orientation of the shape.
The "overworld" segment doesn't really add anything to the game except showing us Timmy. We love Timmy of course, I love Timmy so much that I'd like to be able to walk diagonally towards him.