My usual feelings about letting bottom-dwellers upset their way to the championship apply to conference tournaments as well. The Big Twelve and SEC each have two divisions; this results in somewhat less comparable conference records between the divisions because teams from different divisions have played different schedules; even within a division different teams have played different schedules, even if this only applies to home vs away, as it does in basketball. I think teams should be seeded into the tournament by their record in the division first, with conference record as a tiebreak (N is north, S is south):
N1 vs S2S1 vs N2
N3 vs S4S3 vs N4
N5 vs S6S5 vs N6
This is the first round; in the second round, the loser of each game plays the winner of the game listed below it, while the losers of the bottom two games play each other, as do the winners of the top two games.

That's it. Two rounds. The top two teams in each division are the only ones eligible for the championship; the championship game, assuming the seeding was done properly and no upsets occur, will feature the two best teams in the conference. Other teams, perhaps NCAA bubble teams, get a chance to play themselves up or down a few positions in the conference rankings; these games are mostly for pride, and to give the NCAA selection committee a good look at the bubble teams playing against each other.

I have some concern that three teams will end up 8-2 atop one division and that one of these three is denied a shot at the championship because of a tiebreak. A better tiebreak in some of these situations may be to play a playoff (before the tournament) the way the Ivy League does for its championship (since the league doesn't have a tournament).