Such a neat mechanic! I like games that derive from one mechanic but can make for deep and interesting levels. Good job. That is also why I created a puzzle game for LD46 myself.
If I can give you one point of feedback: The baby crawled through the spike (which isn't game breaking). And I didn't expect it to fall from a tile because at the borders it will swap his crawl direction. But those are really small things and with trial and error I eventually knew what the rules were. But nevertheless, really great and polished game!