Let's assume the first part of the prediction is correct, that they lose Texas and Oklahoma, but then nobody else (which means keeping West Virginia, which is tough for BYU).

At that point, UCF and Cincy are the clear top two choices. Houston probably also becomes tenable as they want more Texas representation and don't have to worry about mucking things up for the big names in Texas since they'd all be in the SEC.

So then you've got BYU vs Memphis for that last spot, which is closer than we might think

History/Prestige: Big Plus for BYU
BYU is absolutely the bigger name, Memphis has had a few strong seasons over the last decade or so, but history before that is...not there or bad. BYU hasn't been great recently, but they're still a well-known name.

Geography: Huge plus for Memphis 
BYU would average 1350 miles from each of the other schools. The closest (and only within a thousand miles) would be Texas Tech (870) miles and they'd have West Virginia at 1950 miles and UCF at 2350 miles. The furthest road trip for Memphis is 830 miles (UCF) and the average is only 600.

Current on-field success: Slight plus for BYU
Over the last decade, BYU has been ranked 20 total weeks and finished ranked once (at #11). BYU has won 60% of their games, including 39.5% against P5/ND. Memphis has been ranked 21 total weeks and finished ranked 3 times (#15 at highest). They've won 56% of their games including 37.5% against P5/ND.

Fanbase: Push
BYU lays claim to a larger fanbase, but a lot of them are LDS members who don't attend, watch or support the team. Over the last 4 seasons, BYU football has had 36 nationally televised games, which have been watched by 38M viewers.  Memphis has had 30 nationally televised games, which have been watched by 45M viewers (50% more per appearance).  Locally speaking, BYU has 2.7M people within 100 miles, whereas Memphis has 2.6M.  BYU's area is showing much more growth though, and BYU has the substantially larger student body.  Give the edge to Memphis on TV ratings, BYU on local factors, call it a push overall.

Off-field issues: Push?
Frankly, this depends on how things are weighted.  BYU has the LGBT issues and the association with the church that hurts them in many corners.  Memphis has a history of violations.  

Given all of the above, I do think BYU is the stronger choice.  But I worry the religious aspects could bump Memphis over them.  Ignoring the religious aspects, UCF and Cincy probably have a stronger resume for the Big 12 than BYU does.  Houston and BYU are about equal, and Memphis (or Boise or UNLV or SMU or whoever) is clearly worse.

I've numerous times said that we place too much blame on religious aspects for why we aren't in.  But choosing Memphis over BYU would be a clear indication of that being decisive in that case.