One of the interesting thing about the English language is its evolution. I don’t talk like my grandmother, and she probably doesn’t talk like her grandmother did. My accent isn’t as noticeable as hers, at any rate. The same can be said when comparing any two people from different generations.
What about the accents of the first Americans? They definitely didn’t speak in the same way we do today; one look at the Constitution tells us that. But what about their spoken language? At this point American and British accents hadn’t diverged into what we know as American and British accents. This isn’t surprising. What we know as the American accent today is closer to what early Americans spoke than today’s British accent is.
So if you really want to sound like an early American or a 16th century English citizen, don’t bother polishing your British accent.