Here’s how I would do it:
After each round, take most of the players from the winning team (say 8 out of 10) and the top few from the losing team (ie, 2 out of 10), and split them up randomly for the next round. Just use the number of caps as the score, since that’s the way the player list is sorted already. I can’t imagine 1v1 would be terribly fun, so maybe we should stop at 2v2 or 4v4 and give prizes/whatever to the winning team.