Remembering that the 6 duplicate schools need to be in opposite Conferences, and that 6 duplicate owners also need to be in opposite Conferences, the below is the best I could come-up with. Please comment with any concerns. If commenting, remember to include your proposed solution. Thanks.
Cincy - onsl(2)
UCLA(2) - all(2)
UNLV - rubn(2)
NC(1) - logain
Duke(1) - cool
Mich(1) - klinke
Ky(2) - cmc(2)
Kan(2) - krish
Fla - sr(2)
LSU - bfan(1)
Okla - Galv
Tex - jhs
Ky(1) - cmc(1)
Kan(1) - eleib
Houst - sr(1)
NC(2) - mcd
Duke(2) - badja
Wake - onsl(1)
UCLA(1) - poppa
Ore St - seap
Ariz - alog
Ariz St - rubn(1)
ND - all(1)
Mich(2) - bfan(2)