Why not rebuild the Big East?
What if the Big East were two parts, call it blue and red. One part is only basketball and olympic sports. The other part has FBS football. Take Nova and Butler and move them to the football side, requiring an upgrade of course. Add UConn, Cincinnati and Temple from the AAC. Add three more teams. Perhaps one could be Memphis but I would try to avoid travel issues and Memphis is getting pretty far away. Other options could be UMass, Navy, Army, Buffalo. Even Toledo or Ohio could work.
But I would lean toward Army and Navy to boost the academics and character. Then you could add UMass to get a MA team or Buffalo to get a NY team. Or, if Army doesn't want to join, take both. I prefer that to grabbing teams from the deep south. Enough of that. We will never be the SEC or ACC.
So the Big East Red would be the current Big East minus Villanova and Butler. Big East Blue would be Villanova, Butler, UConn, Cinci, Temple, Navy and two of Army, Buffalo and UMass.