I still feel the best teams for the Big East to invite are Temple and Tulsa, both for all-sports. Both have had success on the football field (Temple on the upswing), both are competitive in basketball and both offer bigger markets than any of the other teams out there including FCS teams that may or may not want to move up.
Tulsa adds a western team to help bridge the distance between Boise & SDSU while Temple, being a former member, adds more of the Philly market and is a geographic fit. I lean towards Tulsa just because it evens out the divisions more than adding Temple although I don't think you can go wrong with either one.
Tulsa would be a great add for the divisional alignment, the relative success of the program (Their stadium might be an issue though). I don't know why they went with Navy over Tulsa (except to get a chunk of the Army/Navy game in their TV deal?).
Here's the thing, though. They're at 12 football teams and 17 basketball teams. Now, they can do one game vs everyone and two rivalry games in hoops; but adding two more all-sports members makes it 14 and 19. And the odd number of hoops teams can make scheduling difficult (since someone is off on every Saturday).
If they went with Charlotte, they'd be at 12 and 18 (Or Charlotte, Tulsa and Temple for 14 / 20; but Nova would flip out about Temple). And if Louisville, UConn, Rutgers or someone leaves, they have a pair of upgrades in house.