You point out that Wyoming is an associate member of the Big 12 for wrestling. But that doesn't mean that they're listed as Big12 and then have no interaction or association with them. They go wrestle against them.

Similarly Notre Dame has a scheduling agreement with the ACC, and their NBC contract goes into the ACC pool.

If BYU wants to be an associate member of a conference, they would likely have to do similar and actually be in the conference to some extent - financially and scheduling-wise. Maybe you can limit it to 5 Sun Belt games per season, and shared finances, but that kind of defeats the purpose.