The obvious, easiest solution to overcoming those issues is joining the B12 as a FB-only member.
Sunday play is not an issue with FB, and with the relatively small number of games played, geography is a fairly inconsequential issue for FB. These are both much bigger issues for the smaller sports, particularly the Olympic sports.
So why not push for FB-only membership?
There's another positive to FB-only membership. For those who are opposed to BYU based on "cultural" factors, FB-only allows them to say that BYU is a limited member of the conference.
I'd be all in with a FB-only invite, especially if it included some sort of scheduling agreement for BB.