Here's my thoughts on what I consider traditional rivals in our new conference:
Alabama - Auburn/Tenn
Auburn - Alabama
Ole Miss - LSU/Miss Lite
Miss Lite - Ole Miss
Arkansas - LSU/TAMU
LSU - Arkansas/Tamu/Ole Miss
TAMU - Arkansas/LSU
Tenn - Vandy/Alabama/Florida
Vandy - Tenn
SCAR - ? Us now I guess. Maybe Florida too because of the Visor, but whatever. (I still think their true rival is NCst and UNC)
Florida - Tenn and (FSU)
Kentucky - Tenn
UGA - Florida and (Georgia Tech)
Mizzou - ? but really (Kansas) A good fit IMO would be SCAR though. With the exception of basketball, the two programs are on par with eachother.
How close am I on this?
I completely understand the reasoning behind some of your explinations that Bama and LSU are rivals, Florida and Bama, so on and so forth, but its my understanding historically, this is how it really was/is/should be. Of course, the two top tier programs are going to be "considered rivals" based on the magnitude of the game in which they face eachother. Geographically and historically speaking though, this is how I see it and always have.
Impressive, you've got a lot of it but there were a few you missed.
Auburn and UGA both consider each other fairly big rivals; it's nicknamed *" the deep south's oldest rivalry" as well as one of the reasons the permanent cross-division opponents set up was created.
UF also considers UGA big rivals (world's largest outdoor party game).
Auburn and LSU are pretty big rivals with each other, though I'm uncertain how historic (/long) the rivalry is
If you're including Vandy for TN, then UK also needs to be there; it was a game played for a trophy (a painted wooden beer barrel) until the late 90s.
Someone else said UK and Louisville are rivals.
South Carolina - though still having some once and a while ties to UNC and NC st - would most likely have Clemson as their biggest rival (the "UF-USC" idea is kinda stretched though the same way as you claim "LSU-Bama" to not fit fully).
I'm not certain how big ole miss and LSU are to each other rivalry wise (just not fully familiar with the two programs); if so though, Miss St and AL fall under some similar lines, though I couldn't tell you how reciprocated that one is by each side.
One worth note - though hard to gauge due to the sizes of the schools - would be Ole Miss-Vandy. The two have played 86 times, the last 53 years in a row (and 67 of the last 68 years). I can't tell you how highly they regard each other as rivals.
Missouri's likely playing Arky yearly so that should develop as one...some others more than likely will come relative to performances