It's hard to imagine that every community was such a cultural melting pot that the accent was watered down everywhere in America.
The "British accent" you're talking about is a very localized accent found in Britain that has become the prestige accent over the last century or so, distinct but influenced by the rest of the accents in Britain. It is not a constant thing; no British people 230 years ago spoke in that accent. So your assumption that no American accent today resembles that old British accent is wrong; we can't know whether that's true or not because recordings do not exist.
Secondly, languages diverge. Like with Britain, the accents in the U.S. are constantly influenced (especially with the rise of transportation and connection by railroads, wagons, etc.) by other accents from the rest of the U.S. So the British accent was not "watered down", but both the British and the American ways of pronouncing things diverged because of the Atlantic Ocean and national sovereignty. Neither of them are more "original" than the other.
The accents in America may be more influenced by foreign immigrants and the founder effect of what part of Britain the original British colonials (later Americans) came from, but Britain is also close to Europe and Ireland, and 400 years ago hosted a wider diversity of regional British dialects than America due to the lack of quick transportation and terrain and the founder effect leading to only a few of those dialects making it over to America, and the modern Received Pronunciation ("typical British accent") will have been influenced by those dialects and languages since then.
There's always room for more answers, but you may be interested in the relevant section of our FAQs while you wait. The abbreviated version is that there were (and continue to be) a variety of British and American accents. The ancestor of the accent that Americans currently associate with Britain was not the dominant one among the early American colonists. To be more specific, the colonial accent, like most modern American accents, was rhotic, while the familiar "British accent" today is non-rhotic. Non-rhotic accents became more common in England after the Revolution.