The schedules are not concrete, and have plenty of flexibility for something like this, particularly if you are just talking about manipulating the cross division games. We would just need two weekends to be open for home and away dates against TBD......and TBD would be determined as soon as the season is over.
BUT, as long as Auburn and Alabama want to hang on to their precious rivalries against UT and UGA, this won't happen.
Except that I think those teams could just play each other as non-conference games. For example, any year that Alabama wasn't scheduled to play UT, those two teams could still play each other as their "non-conference" game against a major conference opponent. I know Alabama played UMiss a couple times in the 70s in games that did not count in the SEC standings, so they could just do that again with UT.