The 3-6-6 works well & has a few variations. The 1-7-7 would almost have to be a non-starter since ESPN will require 9 conference games if they're going to get anywhere close to the B1G TV deal when they renegotiate with UT/OU having joined. My list of permanent opponents is probably more skewed to recent rivalries that I enjoy watching but it does keep the biggest games on the books which is what you want for TV $$$ purposes. The biggest one I go back & forth on is the LSU/a&m game. Obviously this is the one game a&m will moan and groan about but if you give them OU & take the Ole miss game & give it to LSU that would restore one of the longer ones while simultaneously pissing a&m off. Ultimately, I think that game stays (they do have 60 meetings so it has some history) & OU/Ole Miss becomes a forced rivalry.
Bama: Auburn, Tenn, LSU
Arky: UT, a&m, Mizzou
Auburn: Bama, UGA, MSU.
UF: UGA, LSU, KU
UGA: UF, Auburn, SC
KU: Tenn, UF, MSU
LSU: Bama, a&m, UF
MSU: Ole Miss, Auburn, KU
Mizzou: OU, Arky, SC
Ole Miss: MSU, Vandy, OU
OU: UT, Mizzou, Ole Miss
SC: UGA, Vandy, Mizzou
Tenn: UK, Bama, UF
UT: OU, Arky, a&m
a&m: UT, Arky, LSU
Vandy: Tenn, SC, Ole Miss
UT 2024: CSU, Michigan, UTSA, @UGA, Mizzou, @OU (dallas), BYE, @LSU, @Arky, MSU, @Vandy, @Auburn, a&m
UT 2025: @OSU, San Jose St., UTEP, UF, @Ole Miss, arky, OU (dallas), BYE, Bama, @SC, UK, @Tennessee, @a&m
UT 2026: TXST, OSU, UTSA, UGA, @Mizzou, @OU (dallas), BYE, LSU, @arky, Vandy, @MSU, Auburn, a&m (look at that home slate)
UT 2027: Rice, @Michigan, UTEP, @UF, Ole Miss, arky, OU (dallas), BYE, @Bama, SC, @UK, Tennessee, @a&m
As much as I just love welcoming & visiting TTU, ISU, KU, BU, TCU, OSU, WVU, & KSU I think maybe... just maybe... UGA, UF, LSU, Bama, Tenn, Ole Miss, Auburn, arky, & a&m will make up for those losses.