It would take 9 games, but it could look like this (assuming two East division pods and two West division pods:
3 games inside the pod. Two rotating games against the other pod in your division that are offset by one year. The other four games your pod plays one of the other two pods home and home then swaps.
So let's say it the pods you named and we are talking about UF.
Annual games against UGaly, UK, and USC.
For the second pod on our side, in year one let's say it's home against Auburn and away against Bama. Then in year two it's home against Bama and away against UT. Then in year three it's home against UT and away against Vandy, and in year four it's home against Vandy and away against Auburn. Lather, rinse, repeat.
For the 2 pods on the other side, it's home and home against Pod A then home and home against pod B.
What this does is give us a home and home against every team in every other pod every 4 years. It also gives us a minimum of seven common games with all our podmates. In fact, we could have all nine games in common with one other podmate if we were on the same rotation with them, would just have reversed home and aways with the other pod on our side. So we could literally eliminate the constant schedule advantage UGa seems to get over us almost every year.
Finally, this gives us a schedule that has one different opponent one year, then 5 different opponents the next year, then 1, then 5, etc etc.