Just in case anyone wonders why I would put so much energy into something like this.... it is because I didn't. It took less than 45 minutes. So yes, Spurrier, it can be done.
What you see below is a random attempt to change the current system and make everyone happy. This is my first time doing a fan post and I am unfamiliar with all the editing options, so I do apologize if the table does not look all too great.
What I did was organize the 14 teams into 4 divisions. They wouldn't actually be real divisions, but simply football pairings of which a program would be grouped with. The 4 'divisions' are as follows:
A. Florida, Georgia, Carolina, Kentucky
B. Auburn, Alabama, Tennessee
C. Missouri, Vandy, Ole Miss, Mississippi State
D. LSU, Arkansas, Texas A&M
Honestly, these groups can be paired up in any way, shape, or form, but these four are for the most part respecting the demands. They are a combination of geographical opponents as well as historical match ups.
Every division team will play all of their division opponents NFL style. They will ALSO have at least one permanent rival from every other division. That way the Florida/Tennessee's and the Georgia/Auburn's of the world will still be able to continue on playing. Certainly not every rivalry can be accounted for... but I did my best to pair the divisions up to keep the most important ones alive.
The 1's in the table account for permanent rivals. I wanted to make sure that everyone had a total of 6 while being able to have 2 non divisional games for home/away rotation. If you go through the lists, I hope you'll find that the SOS for each team is for the most part relatively balanced (except KY..... sorry KY, but with all due respect, you ended up mostly with teams from the East anyway so it's not like much is changing.)
Not that Slive is about to call me and ask for permission to use this format, but my point is that there ARE ways of making everyone happy, whether it's this random fan's schedule idea or the next. Furthermore, as far as dealing with who goes to Atlanta, these aren't real divisions, so the two teams with the best conference records and football playoff national rankings will be the two teams left standing (See Pac-10, and old B1G... or current B-12).
Here is an additional chart that has Kentucky and Tennessee reversed and also shows an example of rotating match ups (counted at '2' to distinguish from permanent '1' opponents)