Your challenge is to have an enlightenment revolution a la the American and French Revolutions, take place in both Britain and America. Bonus points if they are still part of the same country afterwards.
Perhaps, after the revolution, Britain lowers the American taxes, but actually collects them; they also crush anti-British propaganda by making it well known when they have good intentions, such as explaining that the tea act was just to stop people from overpaying for smuggled tea.
EDIT: also make them equally as kind to the majority inhabitants their colonies as to the governors, and as to the British citizens.
It's very plausible, but you need someone is an expert on politics in Britain and America between 1750 and 1800 to pull it off. We've lots of people here on this site in one or the other but not so many who are experts in both.
I'm still rather surprised a major timeline on such a subject hasn't been written however.