[Andrew]

One of the ideas that was mentioned last year when this problem manifested was to generate a list of matches that had all of the good characteristics (time between matches, good "randomness" of matches) for n teams, where n = 24, 25, ...55, 56, 57, ...

Then, at the competition, randomly map the teams at the competition to the match list.

In other words, Generic Team 1 = Team 356, Generic Team 2 = Team 400, Generic Team 3 = Team 25, etc.