A really fun idea! I can easily see this back in the day on coolmath or newgrounds. Feels like if Ultimate Chicken Horse was a flash game.
It was a lot of fun to play and having your past decisions add to the puzzle makes it all the more satisfying to solve!
I do wish the bush or some new item could delete/cover up goat heads or other objects. Made it to level 8 and had goat heads placed at the exact spot of the trampoline >_<. Definitely my own fault though but the ability to delete an object could create some interesting player decisions.
Loved the graphics from the moment I saw Dr. Xavier. Reminds me of Little Big Planet stickers. Nice sound effects too!