Can individual players participate in the team tournament?
If the tournament hasn't started, the team captains haven't assembled their teams, and adherence to templates isn't a defining feature of our tournaments (which it really isn't), can we try to find a place for like-minded individuals? We're not giving away gold, after all:)
What if the number of participants isn't a multiple, so a player who doesn't make it onto a team still participates in the general competition, earning points for their individual score? Since it's a "one-shot" deal, and pairings are generated randomly, we can randomly generate matches and assign non-team participants to them. If a replacement is needed, the solo player can be assigned to a team, possibly with the points they've already earned.
I don't want to wait another week. I'm suggesting a combination of versions of "The Restoration of Erathia" in the tournament. If it's going to be much longer.