I think you have three options.
1. Strictly enforce the rule of be a member or do not compete. Kinda harsh aint it? It can do more damage than good in the long run, pushing people away will leave them bitter.

2. Be lenient and do not enforce anything, if they win then make sure they are members. But then its a catch two because we are not enforcing the rules.

3. Leadership - My favorite. if my subordinate fails I have failed him. A good leader makes sure his people are setup as much as possible to be succesful. If I were area rep, I would start tagging folks early on. I would surely get in touch with the regulars who have a chance at winning the event. I would make sure the top 10 teams are registered and all their paperwork is good to go. I would then work hard on the rest to make sure they show up and give them all the options available.