Washington probably had something close to a Virginia Tidewater accent today, one of the older American accents (based on the isolated Chesapeake communities like Tangier Island that speak the strongest version of it) - a kind of softer, more aristocratic, maybe more "British" version of a Southern accent, with some pronunciation idiosynchrasies like "oot" for out and "hoos" for house.

As for the 18th century Brits, wasn't that right around the time today's "Queen's English" accent started really taking hold, especially among the elites? In that case, E:TW should probably err on the side of traditional "British" accents for the British characters, and modern American ones for the American characters (but if George Washington has a Virginia Tidewater accent, I will be very happy).