I would prefer a normal 3v3 tournament above a national tournament.. I guess I wasn't the only one who said that. All these thoughts about random alliances kind of put me off, just go for a normal 3v3 tournament then, it's probably a bit harder to organize but definitely more fun imo

If you're scared of overpowered teams, rank each player (rank A, B and C) and put one of each together . Or have every player choose one of each rank so that it could work out anyway AND be rather even.
Ah, and perhaps a rank D, cause 4 players a team would definitely be a must.