Actually, it was done July 1776, or just before (can’t recall the detail, but they moved out before August).
It doesn’t matter what the facts are. If people aren’t given all the facts, and are mostly given impressions - well, their impressions will be less than factual.
Surely you’ve heard the saying “if you repeat a lie long enough, it’ll be true”.
The last fight of any import in New England during the Revolutionary War was Bunker (Breed's) Hill, which occurred on 17 June 1775, about two months after the Battle of Lexington and Concord. The British were so depleted after Bunker Hill that they withdrew to the island of Boston; New England militias were able to keep the British bottled up in Boston until March 1776, when the British evacuated to Halifax.
That's just straight history. I find it hard to believe anyone thinks the Revolutionary War was fought entirely in New England, as you claim. I think, rather, you were just looking to take some pot-shots at New England.