I just finished playing the game, what can I say, I really like the idea. The fact that you have to figure out exactly where to 'die' in order to use yourself to climb is a very fun concept, and I actually enjoyed completing the levels.
The graphic style it's a bit weird but it reminds me a lot of old flash games we used to play back in the day, it is charming in its own way and brings back some memories.
If I could give a suggestion, maybe consider adding a limit to the number of loops the player can do. It could offer a different layer of difficulty, since from what I played, they seem to be unlimited.
Anyway, really interesting idea! :)