In constructed Magic: The Gathering, going first is an advantage (at some points in history, a gigantic one). Their giant tournaments that pay good money do not use who went first as a ranking tiebreaker and never have. What they use is:
1. Match points
2. Opponents’ match-win percentage
3. Game-win percentage
4. Opponents’ game-win percentage
#1 is just how well you're doing, don't be fooled. #2 is a nice tiebreaker, did you play against people who are doing well. There's more data there in Swiss than in single-elim but it's still something. After that they devalue draws in case that helps.
One thing to consider is, what will feel satisfying in the finals. Here it is, the finals. It goes to a 7th game and it's a tie. People are obviously going to want to see an 8th game played. But no, we need to wrap things up, 7 games is plenty, someone argues somehow. What tiebreaker could you possibly use there that wouldn't feel awful and stupid? I put it to you that the regular Dominion tiebreaker of fewest turns is the only thing even remotely acceptable. Anything else and it's, why didn't you have a real championship. There is more attention paid to the finals than to the semi-finals, more to the semi-finals than to round one. Still if it's obviously bad in the finals, why is it acceptable earlier? Those earlier games also decide who wins the championship. The finals match-up could have easily been the semi-finals instead due to how the pairings fell out. If there's a dark horse, a new online player that seeding doesn't place appropriately by skill level, the finals match-up could have happened instead in round one.
I do think it would be reasonable to let the players decide what to do after the 7th game. If both want to play the 8th game, they play it. If neither does, they use the tiebreakers (turns, match record, ranking; you could throw in opponents' match record before ranking). If just one does, that player wins the "they wanted it more" tiebreaker. I like that tiebreaker because it's right in line with the kind of person who will do well in the tournament anyway: the kind that plays a ton of Dominion. If you don't have time for an 8th game, I don't see how you had time to play enough to be good enough to make the finals.