OK, let's try this. Remember, 7 owners have 2 teams which need to be in separate Conferences, and 5 teams were used twice and need to be in separate Conferences.
Atlantic-
shine(2) - UConn
redb(2) - Gtown
robb - GTech
sappy(1) - UNC
robusk(2) - Wake(1)
creigel - ND(2)
Central -
cmc(1) - KY(1)
fii - Kansas(2)
all(2) - Illinois
sam - Louisville
ben - HS(1)
miles(2) - Foreign
MW-
cmc(2) - KY(2)
shine(1) - Mich
redb(1) - Kansas(1)
twins - Mich. St
sappy(2) - Texas
master - Iowa St
Pac -
ncold - UCLA
rubn -Ariz St
robusk(1) - Ariz
shadow - Wake(2)
all(1) - ND(1)
mile(1) - HS(2)
Of course there are placements I don't love, but given everything, I think it's not too bad. I'm certainly open to suggestions for improvement, but please make them complete solutions and not just things like "ND isn't Pacific". That really doesn't help.