I've actually wondered the same thing. Personally, I try to imagine her with a very slight Boston accent, but it always ends up sounding Midwestern (i.e. "Standard American") in my head since that's my accent. I imagine all of the 1776 as having accents somewhere between modern American and RP British for some reason, except for Knowlton, who has a fully American accent, and Bea, who has the same accent in both centuries. I'm not sure how any of them are supposed to sound, though, and I didn't really put that much thought into their "voices".
Also, for whatever it's worth, I'm a mezzo-soprano and I sang "Think of Me" for a recital, high notes and all. I do agree that Bea is probably a soprano, though.