This is where I think a sign up sheet might come in handy. You could predetermine certain individuals that you would not want on the same team.
Another thing we could do is go back through the logs of previous KOTH's, I am assuming most players would come from these ranks, and rate each player as potentially an A,B,C, or D player based on the perception of their abilities. You have that list available at the start, and as you either form teams or check off pre-formed teams, you make sure you don't have teams with 2 or 3 A players. I would say, for instance, anyone who has won a KOTH would be an A player. Anyone having won a round is a B player. Any player with close to at least a 1 to 1 K/D ration IN KOTH is a C player. Newbs and players with .5 K/D's and lower are D players.
If we are going to assume that the only way to make fair teams is to place people on teams as opposed to pre-formed teams, then you are going to have to have help. You should get 2 or 3 others who will defanitely make the event and ask that they help keep track of and form teams. These should be people who have a working knowledge of the player base and those that can be objective in rating other pilots. We just want to get relatively fair teams, not insult people.
In any event, I think a pre-event sign up sheet is a good start. Although I think it is important to make it clear that you are still welcome to the event even if you are not on the signup sheet.
I also think it should be stressed that skill level is unimportant, that you will be placed on a team and that it's not a requirement for you to be in a squad to participate.
After the first one of these, the next ones will require less pre-event maintainance, but I think proper preparation for this initial TEAM KOTH will be important to ensure success.