The shortage of refs isn't a quick fix.
I think the assignors and teams need to try to coordinate certain days for certain classifications and give them the priority. A and AA on Mondays and Wednesdays and AAA-AAAAA on Tuesday, Thursday and Friday, or something like that.
You do realize there are more teams in 3A - 5A than the A/AA divisions right? Also why as a 2A team should I always play on a Monday for Region. I did that this season and I feel like it's bogus. If you're going to go that route then let 1A Schools do their games on Monday/Wednesday. 2A/4A get Tuesday/Thursday. 3A/5A get Monday/Wednesday/Friday.