I offer this as an alternate proposal to what we have now and Chad's proposal.
In D1 go back to 8 sectionals with as close to 16 COMPLETE as you can get. The first 2 teams in each sectional automatically qualify to state as in the past. The field of 20 will be filled out by a committee of 4- D1 coaches who have already qualified a team. Their job is to pick 4 wildcards using the ranking and also their experience with running against some of the bubble teams.
In D2 and D3 you would go back to 6 sectionals qualifying 2 from each and then filling out the 16 team field with 4 wildcards picked in a fashion as mentioned about in D1 except using qualifying coaches from their respective divisions. Another possibility is to have 7 sectionals with only 2 wildcards for D2 and D3. This way no bubble team coach will be on the selection committees.