My idea sounds strange, but I think it's the best available.
We have three desires:
1. Play each team in your division for a true champion
2. Play your main rival each year
3. Play every team in the entire conference at least once every 3-4 years.
With eight team divisions, anyone who is split from a major rival (like UGA/Auburn, UT/Bama, or Florida/LSU) needs a dedicated rivalry game. We'd also need 7 games within the division. So in order to play each team from the other division just once every SEVEN years, we'd need nine conference games. To play them once every four, we'd need ten! This is the motivation behind my idea (h/t The Only Colors).
Add, for the sake of argument, VT, Clemson, Georgia Tech, Florida State.
Divide the conference into four divisions:
Georgia/Florida division:
UGA
GT
UF
FSU
Eastern division:
USC
Clemson
VT
Kentucky
Tennessee/Alabama division:
UT
Bama
Auburn
Vandy
Western division:
Ole Miss
MSU
Arkansas
LSU
Now, each year, combine the divisions into two groups, making two eight-team divisions. Play each team within your division once (for seven games), and one designated rival. Here's the trick: rotate the groupings each year! That way, you play your rival each year, you play each team in your four-team division each year, but the other four teams on your schedule rotate on a yearly basis. Yet each division still has a champion, and there's a legit conference champion instead of a four-team playoff.
I know it sounds crazy, but I think this would be the best way to handle expansion. That said, I think 12 teams is ideal.