Really smart concept of limiting the amount of button presses. i have not been able to play through, but will definitely do so later! The game is very well working mechanically and super fun.
Spoilers ahead:
While I like the Idea of optimizing across level boundries, and tricks like holding jump, it gets a little frustrating to start compleatly over, because you made a small mistake. Also having to quit and restart the game everytime is a cute gimmick, but doesn't help the problem. Maybe it would be possible to group a few levels and then give a checkpoint / reset the counter? Or maybe I just wasn't there jet xD
Anyways, it a really nice concept, and execution and overall a fun game.
My submission: https://itch.io/jam/gmtk-2020/rate/694239