The key is Ole Miss winning. If we're tied with them, we will lose whatever tiebreaker used since they swept us.
If we beat Mizzou, Ole Miss wins, Bama loses and UK splits, then the top 3 spots would be locked up and there would be a tie for 4th. We would win that tie-breaker as well since we'd be 2-1 vs. Bama and Mizzou, while Bama would be 1-2, and Mizzou 1-1.
If we beat Mizzou, Ole Miss wins, UK loses both, and Bama wins. We would be tied with UK and Mizzou. We would also win that tie-breaker. Both us and UK would have 2-1 records among the three tied schools, but since we beat Florida once, that would give us the edge.
So there are a couple scenarios in which we could get a double bye, but they all involve Ole Miss winning.
What we need to cheer for: obviously a UT win, an Ole Miss victory, and for Bama and UK to go 1-2 combined.