I had considered running a "best of the rest" bracket after the first round for the first round losers. I decided against that as it wouldn't be fair to do that for the first round losers and not the second round, third round, etc.
If you're having fun though, I would encourage you to arrange an informal duel with the loser of the (other) bracket that you would have faced had you won. That way at least everone gets a couple of rounds of duels in although there would be nothing official about the losers duels.
Just a way to extend the fun a little and give everyone another excuse to visit the DA.