This is a pretty simple market demand vs supply issue so the only way to solve the issue is to increase supply (judging sites - qualified judges) or decrease demand (higher entry costs - more work to earn spots).
I personally would like brewers to earn their way to entries by giving back to the AHA community that also helps supply for judging capacity.
Some ideas that come to mind:
1. Volunteer at a NHC Judging site - Earn 1 guaranteed entry
2. Volunteer at another BJCP competition - Earn 1 guaranteed entry
3. Join the AHA - Earn 1 guaranteed entry
4. Place 1, 2, 3 in NHC Round 1 of this year - Earn 1 guaranteed entries next year per beer.
5. Place 1, 2 or 3 in NHC Round 2 of this year - Earn 2 guaranteed entries next year per beer.
6. Other spots could be earned through local competitions that meet AHA guidelines and are pre-approved.
For the items 4 and 5, good brewers could earn the right to more entries next year so that over a few years the best brewers have the best shot at the Ninkasi. A first year entrant would have to work a few years to get up to that level.
Adding some compensation to judges and slightly increasing the entry fees to cover would also help encourage judges to participate.
Just my thoughts.
your suggestions above would result in 30k+ 'guaranteed' entries just from item 3 alone, unless you are suggesting that only new joins would get that (kinda sucks for the lifers or long timers in that case) add in 1 and 2 your going to up that number alot I would think.