I think it's more likely that a shell of the Big 12 invites Big East leftovers to them rather than the other way around.
Rutgers and Connecticut to ACC
West Virginia (along with Texas A&M) to SEC
Louisville, Cincinnati, South Florida, and TCU to Big 12
The basketball schools keep the Big East name. They won't know what the hell to do with it, but at least they have the name.
I'd love for the Big East to become a landing spot for football independents' olympic sports, but I can't see it happening.
Imagine if Texas decided to go independent, and was in the same basketball conference as Notre Dame and BYU, along with our soon to be orphaned seven catholic schools and Xavier.
I think you are pretty much spot on with how the football schools shake out.
I just can't see Texas going independent or BYU forgoing a football conference to be in a hoops only conference although, it would be great to have them.