Much has been said over the course of the season about the consequences of the top 4 conferences champions getting a bye.  I'm here to propose an easy fix to the format.  We can preserve those byes without having to seed the teams as 1-4.  Keep them as the seed they earned based on their ranking, and then fill out the 12 team bracket  accordingly.  This actually keeps all of the first round matchups the same, but it completely rearranges the 2nd round and onward.

Sorry for the ugly formatting.

The interesting consequence here is that since 2 of the first round byes are below the 8 seed, we end up with conference champion matchups in the second round.  If Boise State was ranked 6th, for example, the Game 4 winner (OSU vs Tenn) would swap places in the bracket with Boise State.

For Ohio State, it gives up matchups (assuming chalk) of Tennessee, Texas, Georgia, Oregon.  Texas doesn't get to cake walk through Clemson then Arizona State, similarly PSU has harder matchups as well with SMU then Notre Dame.  I think overall thinks makes the field much more balanced, as it should be, and properly rewards higher ranked teams as any tournament seeding should.

I don't think any other changes to the 12 team format are required.  This by itself fixes every issue, in my opinion.