I would absolutely love a 4 or 5 game scheduling affiliation with the American, especially if it included access to bowl affiliations and basketball.
It would actually be a great balance to have 4 AAC opponents, 4-5 MWC opponents (Utah St., Boise St., plus 2 or 3 of UNLV, Hawaii, SJSU, Fresno St., Nevada, etc.) and 4 P5 opponents (see USC, Stanford, Cal, Utah in November...other P5's in September).
BYU should play in Texas or Florida every other year, regardless, and the AAC affiliation would deliver that with the UCF/USF and SMU/Houston tandems. Occasional games with Cincinnati, Navy, Uconn, and ECU would be fun. Memphis, Tulane, and Temple help to balance out the schedule, without having to play Savannah St. in November (uck!).
I don't think a full membership deal with Olympic sports makes sense for BYU, simply because of geography.
I would propose a 4-game deal, with 2 games in Provo and 2 in AAC territory to be played in October and November. The AAC-affiliated bowls could also select BYU. This would include the Hawaii and Armed Forces bowls, as well as games in Orlando and Tampa (I don't think Birmingham would be that attractive for either BYU or the Compass Bowl). BYU could also get option deals with the Poinsettia Bowl in San Diego and the nameless Fight Hunger bowl, now in Santa Clara, against PAC 12 and MWC opponents.
Similarly, a 4-game-per-year deal with AAC basketball, 2 in Provo, 2 in AAC territory (as long as UConn, Cincy, Houston, and Temple are regulars in the rotation).
That works for me!