Then I think we'd all burn in the fifth circle of hell.
As funny as this statement is, I still need a real reason why it would be a bad idea. A straight-up, double-elimination tournament with random seeding picked out of a hat.
You're actually very flexible with regards to how many people can play. Sixteen or thirty-two would be ideal, but the structure could probably be tweaked to allow for almost any number of entrants (you can change the number of groups or have five players instead of four or whatever).
Five days per debate, two days to judge, slap a week off after the group stages to allow for judges falling behind. Whole thing should be done before the end of the season it started.
Ok, this is cool. But I'm a little annoyed about the initial round-robin, to be honest.