I thought this was a nice little puzzle jamgame. I think you could take this in a lot of directions and be building on a good foundation. Your last level starts down that vein of 'planning' what your next character will do, the time limit is tight enough that it discourages the 'just put a clone on every switch' strategy, and encourages moving your character from switch to switch.
Like Tom says, the game feels like it's wanting for something. I imagine games with these kind of time travel duplicates, ones which remain behind, have been made before - you could try and grab a couple of mechanics from them to mix up the formula more.
As a Jam submission, though, I'd say you did a pretty good job! The content that was there was pleasant and held my interest! Thanks for taking part!