To avoid long waiting times, why not adopt the system tennis tournaments around here use. Players can give times at which that are available for play. Then there is match making according to availability. Then for the next round, the same principle is used: ie if you win a game you update your availability.
Of course, this way, it would take a week to play a tournament. So what? Maybe there would be more participants? Also: a tournament that is held only once a week carries more weight, doesn't it?
And then if there is a separate tournament classification?