Undertaker.: Still a team with 5 2100+ players is tough to beat, random or not random :)

The fairest idea would be round robin, but then there's that annoying amount of games, maybe work them away in time-specified rounds, like a soccer competition? So players get one opponent per team, and after a while (say 1 week) the next round kicks in so they get another opponent from the other teams. A quick player can finish the eight games they get within the one week period.

For short games like Hyper Backgammon the time period can be even shorter. But for longer games like Go they time period should be even a month, and then still will be games running.