It's a difficult position because from a pure basketball standpoint, I agree that UConn is better in the Big East, but it's definitely a non-starter to be an independent in football. BYU can get by with it because Pac-12 teams (who, outside of USC, generally have lower attendance figures than BYU) are willing to play home-and-home series with them (as BYU fans travel very well, so the Pac-12 teams actually make money in their BYU games) and the ESPN contract is enough to get others to fill in their dates. Even then, it's difficult for BYU to do that from year-to-year and that's a school with a nationalized fan base.
So, the only realistic option for UConn that it can actually control itself (i.e. it can't force the Big Ten or ACC to do anything) is to join the MAC as a football-only and the Big East for other sports. I don't know if that sounds really appealing - as much of a mishmash the AAC might be right now, it's still significantly better top-to-bottom than the MAC for football. Faced with that choice, the AAC is still better overall for UConn if the school still believes that it can get to one of the 5 power conferences. Real and perceived football ability and history is what has bogged down UConn in conference realignment, so it can't take a football downgrade if it wants to move to the next level no matter what might happen to basketball. However, if UConn looks in the mirror and thinks that it realistically can't ever get to one of the 5 power conferences in this generation, then that's the only reason why you'd consider the MAC football/Big East basketball option in order to maximize basketball at the expense of football.
Tell me again what drives the bus? You say "Real or perceived football history is what bogged down UConn in conference realignment..."
The P-5 found homes/new homes for Rutgers, Syracuse, Maryland, Louisville, Pittsburgh. Was it because of football prowess? Don't think so. In fact Syracuse was in the midst of a 6 year slide when they got picked up and didn't have a national title since the fifties (about the last time an Ivy league team won one). Rutgers, what legacy did they have? Maryland? Explain? Pittsburgh? A glorious season with Dorsett in the middle 70s (coming up on 40 years ago) - then what? Louisville has been strong lately but had big bumps in the road in last decade. (Further, they provide proof that academic standards don't apply anymore in the ACC.)
Apparently it is something else. Whatever it is, we're not going to find it in the MAC/BE deal you suggest.