How did the early American colonialists slowly lose their accents overtime?

The speech of the various settler groups underwent dialect leveling, a process that results in a brand new accent with some similarities to its parent accents. This same process happens every time speakers from regions with different accents come together - it happened in North America, New Zealand, and Australia with English, in Latin America with Spanish and Portuguese, and in Quebec with French.

Since the time of the dialect leveling, the American accent(s) have continued to evolve, as all living languages including the various British accents do. The accents are wholly American, although they have roots from across the British Isles and some influence from other languages.

Southern accents and Northern accents are cousins. Neither of them is more neutral than the other. It just happens that certain Northern accents became prestigious, thanks to a combination of factors such as wealth. I'm sure that the Civil War played a major part in it.