Seems that, long term, three rounds of judging is going to be the way to go. That would mean you could have lots more smaller/local comps for the first round (and for the second round for that matter).
The problem with another round of competition for the brewer is more bottles would be required. Currently at 4 for beers for those advancing to the second round is already twice the number most competitions require. The problem for the AHA and the site coordinators is another round of organizing, rounding up staff, and the competition itself. I don't think this is the way to go.
As for compensating the judges in some way I am all for that but it must be done fairly for all who participate no matter how far they travel. Perhaps a free entry to judges and stewards (could be counter-productive to limiting the entries though). When I ran the a regional competition a few years ago we provided a BBQ dinner party for the staff after judging that was paid for in our budget. I understand this expense has been DENIED in the past couple of years.