I somehow forgot to tell you how you could solve the checkpoint system. I think it would not be necessary to have a checkpoint for every level. Every second or third level could be sufficient enough to keep the player entertained.
For the music, having a background music for each level would be nice, but too much work for a game jam. Just switching between two music tracks each level should have done the trick. But yeah, we had the same problem with our game.
Maybe you want to stop by and play it ;)
Spoiler: it's also a 2D platformer