I don't think we need to reinvent the wheel. I think we can look at how other states set up their tournaments. I know that North Carolina's team state format uses conference results to determine the teams that are in the tournament. The conference I coached in would get two teams and often would get an at-large bid.
Their set up had 3 classes with I believe 32 team brackets that were seeded (16 in the west and 16 in the east). These teams would have duals/super duals during the week, much like our current team regionals, and then culminate with a final four Saturday.
Conferences may have to move their tournaments up a week or two. But, from my experience, they system seemed to be effective.
I apologize if I'm in error on some of the details. It has been several years since I coached in NC.