I think if you go fulltime and pay well enough, you'll attract an entire new group of refs. Yes, bias exists, but if you grade them out each week, you'll be able to eliminate most of that. I've been a certified ref before, usually most guys are fairly locked into the ongoing play instead of the which team is it mentality.
Paying guys $2k/game means we get half"donkey" refs and not a good supply of replacements. If you paid $100k starting, you could attract tons of football people (high school coaches would jump at this IMO).