How about breaking it into two tournaments. One in the North and the other one in the South. Invite the same number of teams to the two tournaments. Then the top six (or eight) in each North and South tournament qualifies for the State tournament. All teams would wrestle through placement.
This allows more teams to qualify for the North and South tournaments, but the better quality teams to advance to the State tournament.
After thought..... Plus it would really suck traveling 4+ hours and only wrestling 2 matches.