Bill - I must be missing/misunderstanding something, because it seems to me that the right approach here is already indicated by and contained in your original post. Your club already has a good culture regarding pace of play, and an environment in which good natured ribbing is followed by a letter and then followed by restrictions. So why not start by writing a letter to all members prior to a club event, something like (off the top of my head):
Dear Club Member:
One of the many qualities that we all appreciate about our club is its strong tradition of not accepting slow play. We are very fortunate that, unlike most golfers at clubs all across the country, we rarely experience rounds over 4 hours, even on the weekends. I think we all play a role in that, and should be both proud and grateful about it -- we understand and value the etiquette of a proper pace of play, and we care enough about each-other to all do our part in ensuring it.
Some of you may have found, however, that when to comes to intra-club matches that admirable pace of play slows down considerably. As we approach our next club event, it seemed like a good time to remind ourselves of what we already know (and regularly accomplish) regarding a proper pace of play. Granted, we all tend to take a little more time during competitive rounds – but if we can try to stick closer to the good pace of play practices that have earned us our enviable reputation and tradition, we’ll probably all play better golf, enjoy our club events even more, and still manage to get around in 4 hours.