I want to see this as a linear, head-to-head event.
Explaining a bit more: choose some number of participants and randomly place them into a single-elimination tournament format. In each match-up, the two people are seated across from each other and given the same scramble. They have 15 seconds to look at it, then every few seconds (3? 5?) the judge says "turn" and each competitor performs up to one turn, HTM. This happens exactly 20 times. At the end, the competitor with more solved stickers wins. If there is a tie, they go again with a new scramble. If a competitor turns more than once per "turn" or turns at some other time, they forfeit the round. Podium is decided like with any other head-to-head event.