Then people on this board should stop invoking scenarios where the logical conclusion is shutting down the athletic department.
Even the elimination of BCS football at UConn, bumping down to FBS is not even remotely close to "shutting down the athletic department". It puts us back where we were when I attended, except we've won three NCs since then, plus several more in women's hoops and another in Soccer. Not exactly a catastrophe. Playing BCS football as an independent and all other sports in BE is better still.
To put it succinctly, I would rather sacrifice football in a BCS conference than play all sports with a collection of schools ranging from Florida to Idaho and back to New England, mos of which have anything in common with UConn. As you correctly point out, it is an association of member institutions, and I'd choose not to associate with those institutions.
The only scenario I can envision as viable is to drop SFU from the BE for all sports and add no other all sports teams. Then see if UConn and this bizarre cast of extras can all form a football only conference, not called the Big East. SFU, CFU, ECU, Houston, UL, Cincy, WVU, SMU, Boise, , Nevada. Call it the Gumbo conference. It's just a mix of teams that collectively should be able to hold the AQ status. Problem: since this would gut the MWC and CUSA for football, they probably won't allow these teams to play Olympic sports in those conference.