I think any sort of mass cycling event would only exacerbate the situation. What's needed is a bit of diplomacy. The clubs who have received the letter should send representatives to the next parish council meeting. Wear normal clothes, not lycra, so the villagers can see that they are just regular people like them. Be prepared to take a bit of an ear bashing, even if it's not their fault, and then try to discuss the issues properly. Praise the village, invite the villagers to the club socials, condemn the behaviour of the reckless few and show them that their club is made up of safe and considerate people. Maybe try and get a few villagers out on a bike. Get to know each other.
Cooperation rather than confrontation I feel would be the best approach.