Maybe something crazy can be done, if most of these conferences are 14-16 teams:
Lower the necessary OOC games, to only 2. That'll negate the need to find so many scrub teams.
Use the last week or 2 of the regular season for a smaller playoff, inside each conference. Have the 4 best teams play each other, winners go to the CCG, while everyone else is paired with likewise teams in the conference.
As an example:
EAST
Missouri 7-1 12-2
South Carolina 6-2 11-2
Georgia 5-3 8-5
Vanderbilt 4-4 9-4
Florida 3-5 4-8
Tennessee 2-6 5-7
Kentucky 0-8 2-10
WEST
Auburn 7-1 12-2
Alabama 7-1 11-2
LSU 5-3 10-3
Texas A&M 4-4 9-4
Mississippi State 3-5 7-6
Ole Miss 3-5 8-5
Arkansas 0-8 3-9
Auburn play USCe, Alabama play Missouri, then Georgia/LSU, Vandy/A&M, Florida/MSUs or Ole Miss, Tenn/the other Miss school, Kentucky/Ark.
Can leave it up to the back 10 teams to play the extra game if they want to, or some schedule changing in case they've already played that team in the earlier part of the schedule.
If off of the old "8 game conference schedule", this can be a nice way to get everyone a ninth game, while also negating the constant cries of uneven scheduling ("That team didn't play the best teams on the other division and we did"). If used with a 9 game conference schedule, this creates a 10 conference game, further proving which teams are worthy for appearances in CCG's and the National Championship playoff.