I would get rid of the regionals completely and do the tournament the way that has pretty much become standard for conference tournaments.
Same teams make it. 16, with conference champions in. Seed them straight 1-16.
1 plays 16 in a best of three series hosted by 1. 2 hosts 15, 3 hosts 14, etc.
Next weekend, reseed and do the same thing. Best team left hosts the worst in a three game series. 2nd best hosts 2nd worst. So on.
Then the Final 4,where you actually get big crowds and some national interest, is played at a neutral site.
It adds an extra week. It's a dramatic change. But first off, anytime you have a series instead of a game, I think you have a more deserving winner. But secondly, with regionals weekend getting ZERO national publicity and interest and many playing in front of bad crowds, I just don't see the point. Having intense series in front of excited crowds with student sections would be much better marketing for the sport...and a better way to decide a champion.