Looks like Henderson to me too.

Did Broadwood do the case painting in-house or were the instruments finished by a dealer? Henderson is mentioned here as a piano supplier or maker from before 1830:

http://pianogen.org/names.html

and there was a much later piano firm called Henderson, probably unrelated.

Re the Auld Lang Syne tunes: it's interesting that both of them owe their popularity to manufactured culture rather than the autonomous processes of oral tradition. Thomson picked "The Miller's Wedding" tune because it had been made an enormous hit by Shield in his opera Rosina, and the main reason anybody now sings the old tune is that it was used in Sex and the City - which dates from 2008, hence GUEST's estimate of its popularity going back five years.