The solution isn't going to be a simple switch conference fix.
What about a whole new conference all-together. There's a number of good to strong athletic programs in the midwest. All of them tag onto a random conference somewhere else where they don't fit well, either geographically or in terms of caliber. Why not collect all these displaced programs and unite them into one strong centrally located conference?
Programs that would probably want in, and would be a good fit:
SLU
Drake
Dayton
Belmont
Butler
Xavier
Missouri State
Southern Illinois
Memphis (would conference USA really be better? doubtful)
Programs that would fit well, but may not want join:
Northwestern (would have to go independent for football)
Marquette (Big East might be a little bit too EAST for them)
Cincinatti (Big East might be a little bit too BIG for them)
DePaul (Big East might be a little bit too BIG and too EAST for them)
Notre Dame (not as prestigious as the Big East, but it would make playing independent for football easier)
Other programs to consider, but would we really want them?
Murray State (Good Basketball program, but the school doesn't have the prestige)
Wisconsin-Milwaukee (ditto)