There were at least two men named Latham, one the brother of my Hannah Donnell (there were a number of them, too). This one is probably the one you want, as he was born about 1763. The BPC records actually record Charlotte's names in one order in one place and the reverse in another section.
I can get back to this in a couple of weeks, but just don't have time to pull records right now. Maybe someone else can help you in the meantime.
If you want to correspond privately, contact me through
www.benbowfamily.com. I don't have a lot of things on that site, but that is a way to reach me. I don't want to post my email address here, as scanning computers will get it.