I believe there to be zero chance as an at large, and acknowledge that this happens to BYU about once every 30 years.
Like you, I enjoy the schedules that have come with independence. I would like to play 5-6 P5 teams a year, and joining the AAC would make that next to impossible. But is there a middle ground where we get enough P5 schools on the schedule, along with the AAC schedule, that it still "feels" the same? I suspect you're right, that the AAC schedule would take away a lot of the games I've come to appreciate (Wisconsin, Tennessee, USC, Texas, etc.).