Okay...so in reading all of this, a reasonable person (or even me!) comes to the following thoughts:
We have a referee issue. Reasons:
1) There aren't enough referees in total.
2) There aren't enough referees available when games are played.
3) Assignors aren't doing their job.
Several questions:
a) Anything I'm missing?
b) To get more referees and referees available, don't you just pay more (e.g., supply and demand)? If you can't get a referee for a game, or you need an "emergency" referee, can't you handle that in your pay structure?
c) Doesn't this whole "assignor" thing scream out for a simple web-based application or is it more complicated than that?