cool game! Bit of advice from someone who comes from the music industry: this would not fall under fair use. Yes, you made the covers of the songs yourself, but because they sound too similar to the original, it would not be classified as a "remix". Remixes that use copyrighted material need to be considered "something new and original" in order to claim fair use. For a jam, you're probably fine, but if you ever tried to expand on this and sell it, you'd be in some legal issues for sure. It's a clever idea, just be careful when using copyrighted material!
I'd appreciate it if you could play/rate my game as well! :)