Current rules basically state a team needs a simple majority of Masters (7 of 12) to win. It might be a better idea to bump that up to 2/3 (8 of 12) or even 3/4 (9 of 12). The other option is to institute a mandatory minimum numbers of rounds for Stage I, maybe 3 rounds since there are 3 teams. That should have enough time for teams to play at least 1 battle and a potential rematch. At the very minimum 2 rounds is necessary just to ensure that every player is allowed to at least have a battle. I agree that it would be pretty bad to declare a team the winner of Stage I before 1/3 of the events participants even get a chance to play.
There is to say, though, that majority of Champions is a requirement that COULD be tough to get to as it is, if teams were balanced. We have fairly unbalanced teams this time... maybe team randomization would be a better solution. If not, Round 1 could go as long as 10 turns... even more, as Champions get periodically dethroned.
Alternatively, you could say you need to have a certain number of Champions last for a certain number of turns. Not consecutive turns, just turns. The first team to get, say, 7 people that are Champions for 3 turns win the phase. Still potentially unlimited, but not nearly as much.