Richie,
I understand your use of the word 'rare' in the context of its appearance in America, But what surprises me is that it hasn't turned up there much more frequently. Perhaps it has and the collectors simply ignored it because they presumed it was straight out of a book, being such an obvious Scots song. It appears in many collections over here both prior to and after Child's time. It even appears in some Burns collections. There are versions in Gardner and Chickering, Morris, E & C Moore, and as you would expect in some Canadian Collections.

If you go to the Bodl site Douce Prints S 9 (p208) you can see an upmarket broadside with the dots, dated 1785 printed in London, title 'John Blunt'. Pieces of this sort were usually as performed in the theatre.