Instead of limiting the number of entries a person can enter, why not figure out a way for more entries to be handled? From the sound of it, 750 is the maximum that can be handled at one location, so why not split the judging centers. After all why do Belgian Beers need to be judged at the same place as American Lagers, except for logistics? If two places can only handle 500 each, that would still provide a 33% increase in capacity. Even if you limit the number of entries per person, as the AHA grows you'll still have to handle over 750 entries per region.
As for the number of beers needed to win the Ninkasi, anyone could have beat the person who won the Ninkasi with 5 gold medal beers. Even with Gordon Strong and Jamil Zainasheff entering their entire collection of beers on tap.
From the website, points are awarded in a weighted system for medals, and first round points are only considered in case of a tiebreaker. Gold - 6 points, Silver - 4 Points, Bronze - 2 Points
So five gold medals would give you 30 points.
2003 Curt Hausam: 2 Gold, 12 points total
2004 Jamil Zainasheff: 2 Gold, 3 Silver, 1 Bronze, 26 Points
2005 Paul Long: 2 Gold, 12 Points
2006 Joe Formanek: 2 Gold, 1 Silver, 16 Points
2007 Jamil Zainasheff: 3 Gold, 0 Silver, 1 Bronze, 20 Points
2008 Gordon Strong: 2 Gold, 12 Points
2009 Gordon Strong: 2 Gold, 3 Silver, 2 Bronze, 28 Points
So if all you can submit is five entries, it they are all worthy of gold medals, you can win the Ninkasi. Even withpout other people being limited to five entries.
Sorry for the book, but I don't like placing limits on competitions.