Beautiful work, as usual! The only thing I would add is when I get the mixed result, the process would be repeated only on the next turn.
I think this is how I would run it but that distinction is left up to the player’s interpretation. Mostly because trying to visualise this (hard!) moves it away from the simplicity I was after.
I agree, although best of 3 would seem to be good with a single coin toss at the end if a tiebreaker is still needed.