Personally, I hate fly ins. If it's at my club, I'm basically paying to come and fly the same way I would had there not been an event, except I can't use the facility I paid for unless I pay again. It's dumb.
IMHO, if pilots aren't interested in competing at all, then they'll never be pattern pilots. I like competing; it gives me a goal to work toward and an objective standard to measure my progress. I find it hard to believe that there aren't enough competitive people around to get classic pattern flying started in any decently populated area. Are there no former athletes in your clubs? No sports fans? Sure, there may be a perception that it's expensive and time consuming, which may mean they aren't willing to make the commitment. But if you make intro class very beginner friendly and don't let veterans hang around in it just so they can get a trophy it could encourage people to give it a try. A well trimmed Ugly Stick or 4 Star can do intro/novice maneuvers just fine, so there really isn't much of a barrier to entry if you think of it that way.