This whole situation reminds me, as a runner, of the Boston Marathon. For years you had months to sign up before it would reach capacity and close. Slowly, more and more people signed up earlier and eventually, a few years ago, it filled up in a matter on hours (and that's over 20,000 people).
What they started doing was giving the best runners the first few days to sign up, then the next tier of runners get a few days to sign up, and so on until it eventually opens to everyone until completely filled. This ensured that the best runners would have the best chances and most time to sign up. It was all based on previous marathon times.

Pinburgh could work similarly. "A" level players could be given a chance to register first, then "B", "C", and so on. Each can be given a few days to sign up (so the first few days just A can sign up, then the next few days A and B could sign up, then A, B, and C could sign up, etc.) until it fills.

I would also set aside so many positions for newcomers in a lottery type of entry. As a growing hobby, you don't want to turn away new players.

Just my suggestions!