I've made an update addressing some of the issues you pointed out (not the fast-travel though).
Your suggestions are greatly appreciated, I'll keep them in mind for any upcoming games that I make.
Hey pangake,
Been playing couch co-op with a mate and having fun but it appears to block our progression with a glitch where player 2 is stuck in a wall after a transition post double jump being unlocked. P2 being stuck in the wall prevents camera movement and therefore P1 cannot complete the room and drag P2 through the next transition.