The wrap-around system for a platformer is great, and really forces you to think outside your normal platformer-brain. I got to a room with a V and III door I can't reach, a purple dotted line moon box, where it seems like neither Up nor attacking with Z allowed me to affect my environment, but pressing R just sent me back to the position of the purple moon...not really sure where to go at this point.
The sticky walls might work better if you only apply the existing level of stickiness when the player's input is pushing them into the wall (or maybe also for a short duration upon first contact with a wall regardless of inputs, if the goal is to make sequential wall-jumps easier to time), so that they can move vertically more easily.