Hi Rob. Thanks for this interesting transfer! As David pointed out, there were a number of similar equestrian portraits in the 18th century, and as you say yourself, many of these were not so much portraits as representations, that might have been used to portray a number of famous men since the populace at large would not have an idea what they looked like anyway. Having said that, it seems likely to me that this started life as a portrait of Washington - not only the mug you found, clearly from the same source, but information I found online of "fictitious" portraits of Washington. I don't know if I can include this link or not http://web-static.nypl.org/exhibitions/revolution/selection4.html
Which shows this same portrait of Washington, supposedly by an Alexander Campbell of Williamsburg in Virginia, which was widely copied in Europe even during George Washington's lifetime, and which he disavowed. So it seems more likely to be a representation of Washington than of anyone else.