Would make more sense to have 4 teams in winners bracket and 8 start in losers. Losers bracket is single elim, winners bracket losers get pushed down to losers. Winner of losers bracket has to beat the winners bracket winner twice, whereas winners bracket winner only has to win once.

12 vs 5 >winners play 9 vs 8 \ winner plays loser 1v4

10 vs 7 / winner plays loser 2v3 >winners play 11 vs 6 ^winner of losers plays loser of winners bracket for a spot in championship

1 vs 4 loser drops down to losers 3 vs 2 loser drops down to losers ^winners play in winners finals for a spot in the championship game(s)

I’d prefer the traditional playoffs but if you’re looking to change things up I think that would be a cool idea.