A tournament style that might be interesting could be..
For every 5 players, 1 of those players are selected, randomly, as Team captians.
The Team Captians then get decided randomly who chooses first.
After that, the team captians pick pilots from the pool of remaining players in order to make up their team.
Think Dodge Ball.
Example: 15 Players sign up. 3 of those players are randomly chosen to be Team Captians. Then between those 3 players, it is deteremined who gets to pick first. The team Captians then alternate, picking 1 person at a time, until all teams are filled.
After which a tournament schedule would be determined between those teams. And it could be done in one of two ways:
Round robin - Each team plays the other at least once earning points. The team with the most points Wins. In the case of a tie breaker, Tie breaking teams would play each other in a "Sudden Death" match up where the winning team wins the tie.
2 out of 3 Wins: Each team only plays their opponents in one Set, 2 out of 3. Who ever wins those matches advances, the losers are dropped.
That's a cool idea, although the fact that you're picking people at random doesn't sound like it would work good in a protracted tournament setting -- one bad egg kills everything, and if someone becomes a part of a crappy team there isn't much motivation to stay for the long haul.
I think the idea would be most fun if you did that on a weekly basis, perhaps Sunday. Keep it informal. Create as many teams as you can with the participants and have them each take a turn at each other until people get bored. Then create new teams or call it a night.
Cross faction teaming would certainly be a significant help if it were ever to be supported.
In a PVP tournament I would like to see teams that don't warp out and cry once they see that the other team did not bring Mirandas with standard Mk 0 weapons.
And I would like to see a rule that allows the participating teams of an individual match in the tournament to waive any tournament rule. What I mean with this: The rules of the tournament should provide a framework, like e.g. a default time slot for matches if the teams cannot (or do not want to) find a different one. But it should be allowed to simply decide to ignore certain rules if both teams agree - like letting a team use players that they are normally not allowed to use (e.g. from a different tournament team, "banned" players, allow one side to use more than [usually allowed number of players], ...). It should not be necessary to beg the tournament organisers for a special permission - just ask the other team whether they agree.