Disagree that the big east is not a high major conference for basketball. (And you may recollect that it is the current home of the national champions in basketball.)
I think it's dumb for us to define high major as being only football conferences. Seton Hall is a high major basketball program and it has done that under the constraints of being a small private college. Yeah, the "power" conferences in football have a huge amount of advantages, but we haven't been relegated yet. We should go down swinging, not willingly giving up our designation as a high major, which is really a basketball term anyway.