How about this.
Small and mid majors go into top half of bracket. Power conf schools go into bottom half.
Play until there are 8 schools left - 4 from each half of the bracket. Then for the final eight pair a small/mid school against a big school and finish the tourney from there.
My preference would be to play the games on campus of the higher seed. The excitement in those arenas would be next level. Imagine a tourney game at the Barn. What would tickets for that sell for on the secondary markets? A whole lot.
Once get to the final 8 though, play the games at a neutral site.
This format would level the playing field regarding the haves and have nots as well. Mid and small schools would love it.