Thank you all for your insightful responses. I agree in part with all of them, particularly when it comes to free tournaments. Free tournaments provide a great chance for even the most inexperienced beginner to go up against the best players in the club with nothing to lose and everything to gain. Also, using an excel based handicapping system is a fantastic idea that I will probably implement.
The problem that none of these solutions deal with is the "pay for play" tournaments. Even if you keep the cost for these tournaments in the 15 to 25 credit range, if a relatively small number of players always wins those tournaments, then sooner or later they are they only players signing up. What's the point of even bothering? If a real country club did not bother to handicap its tournaments, how many members would sigh up for them?
What I would like to be able to do is create handicapped "pay for play" tournaments which could draw enough players to generate respectably sized pots because many more players felt like they had some semblance of a chance to win. A tournament with 100 players and a prize pool of 2500 credits would be a lot more exciting that a 4 player tournament with a 100 credit pot.
Members would still be free to create and enter "open" tournaments that are not handicapped if that's what they want to do.