Hi All - I've been researching this for some time and with the help of the Kaynors, Ralph Sweet and others, I have now posted a fairly complete history of the song, as much as I've been able to determine it, on the Downtown Amherst (MA) contra dance website. It has the history, links to videos and sheet music.

http://amherstcontra.org/Amherst_Contradance/Birthday_Song.html

Will Loving