Wow this was great. I don't really play a lot of 2d games. But this one felt amazing. The Player controller felt just right (not too slippery and yet not stiff, with the right amount of gravity). The game mechanic of dying and seeing your previous self is amazing. I am not sure if this is a common game mechanic, but I have never seen it before and I must say I think its amazing. Also The music choice is really fitting.
I did encounter 2 bugs:
1) not being able to move next to the moving platform (my player character could look left and right but it was stuck).
2) My player wasn't respawning after it had died.
But you probably already know about those seeing as you mentioned it in your description.
One thing I noticed was that when you try to jump too close to the edge of a platform that your jumps wouldn't register. (Which was what caused many of my deaths.) I feel like adding a bit of coyote time would improve this. Overall great job loved it.