I haven't given this a lot of thought but here's a proposal off the top of my head and I will apply it to the Cincinnati sectionals as an example because that's the region I know best.
Have the 32 teams in this area seed themselves as the now do.
Let teams from 23 though 32 pick their bracket location first but they may only go onto the opening round brackets. #23 gets the first pick and then on down through #32.
Next seeds #1 through #22 pick their bracket locations but only the brackets in the tournament state round of 128 would now be available.
This year Lakota West the number 1 seed played seeds #31 in the initial round & then #32 in the state round of 128 with blow outs of both inevitable. With the system I propose both of these teams (#31 and #32) would not have had to face anybody higher than #23 in the opening round. They would have both probably lost in the first round anyway but would have had much better games. Lakota West would have had to start with a team seeded #23 or better, or at least a first round winner, but also would have probably preferred that rather than having to play #32 and #31.
Last edited by Bob Ashby; 02-27-17 at 07:44 PM.