A rather basic platformer with a fun gimmick. The idea of having a character die-and-repeat is not super new (Reminds me of the game "Life Goes On" and "The Swapper" (to a lesser extent)), but it always fun to see what can be done with it.
Its a 3hour game (I think I got it right this time) so there is only so much time to explore the design-space, you got the basics of it all down but would have been great to see the design more explored. For one, in this game I feel the "go-around-the-edge" part of the design is rather unnecessary, as it has very little impact on the "die-and-repeat" mechanic. There is even one level that does not even use the death mechanic because of it.
I like the ideas you described that could have been added (the eye thing really fits the character design!), but feel even smaller things like: a limited death allowed, limit the amount of corpses at one time, or have them simply dissipate after a while, Just simple things that take the entire "I leave my old body here" into focus and something I need to balance. At the moment it just becomes a mechanic that forces me to replay the same level several times without much timing or skill needed.
Just a side note, love the hat and its animation! Would have loved to see more with it as the focus. maybe after your death the hat stays where you died, and you will die permanently if you don't have the hat on you, forcing you to first collect the hat before dying again.
Overall, I feel just a platformer in 3hours is nuts. So great work :)