Amazing idea, that's the best interpretation of the theme i've seen so far !
The platforming works well but as some people mentioned, is a bit rough on the edges. My games had the exact same problems until I watched that video and implemented the features it describes : Ultimate 2D Platformer Controller in Unity (source code provided)
It's the most counterintuitive ones that have the best effect in terms of game feel, I highly suggest to try and implement them as it improves drastically platforming physics