The match structure depends a bit on the tournament structure.
If you start with swiss, a tie is a perfectly fine result for the swiss phase.
If at some point it's an elimination tournament - you simply need a winner.
If you don't need a winner - I'd suggest the same structure as the league has - just 2 players starting 3 games each.
If you do need a winner I actually suggest the same - 2 players starting 3 games each.
If any player at some point gets to 3.5 points you can simply stop.
If it's 3-3 after 6 games you need something else.
I think I like 1 more game with a random starting player, and if that game ends in a tie the 2nd player is the winner? (I'd still want to be P1 easily)
Another option is to go on playing 2 games until it's not a tie, but that has the disadvantage that it could take very very long.
Quite unrelated: we could discuss making it best of 8 in stead of best of 6 from a certain point on. Maybe semifinals and finals?