Now, you said something about favoring an arrangement that gives every team 'fair' opportunity. I don't know of any such arrangement.
The BCS lets every D-1 school know in advance what they must do to be included in a BCS game. Everyone has access to the system. If you want to be included in the championship game, you have to finish #1 or #2. It may be hard to do, but every team has access.
The BCS, really isn't supposed to be a 'fair' arrangement. What it is, is a competitive arrangement of teams, equally 'qualified'. I simply would arrange them in a fashion that allows one team to win the whole thing.
It really isn't a 'playoff' as much as it is a competitive way to select a national champion.
When you play a group of teams in bracket order to determine a champion, that is called a play-off. You can call it whatever you would like , but it is a play-off.