What I meant was to add two more rounds to your KO instead of having a qualifying event. If that isn't possible, in a swiss system the top half of any scoring group is paired against the bottom half. If the teams have some type of ratings, rankings, or seedings you might have for the 1st round 1-5, 2-6, 3-7, & 4 bye. Assuming all the favs won, the 2nd round would be 1-3, 2-4, 5-7, & 6 bye. This continues for two more rounds and the top four would be your qualifiers. You can research what happens when only one team is left in any one scoring group and tie break systems, but that is outside of the scope of this website forum. The swiss is used quite frequently for chess tournaments.