Not to discourage further discussion, but we have an entire section in the FAQ on American and British accents

• Would Americans at the time of the revolution have spoken with a distinct non-British accent?

• When did the current dialect of American English diverge from traditional British English?

• When did Americans lose their Brittish accent?

• Differences in American and British English accents

• At what point in time did Americans develop an American accent (or accents, for say the north and south)?

See in particular /u/limetom's answer to the last question there.

Side question: what about the southern accent? Was there a distinct accent during the civil war?

There's always room for discussion, but perhaps the section American and British accents in our FAQ located in the sidebar will answer your inquiry.