Evidence seems to point to this song being older...

What evidence, Brían? Sorry, but the only relevant bit seems to be your Irish language teacher saying ...that the GALWAY SHAWL are new words sung to an older melody...

I've got no axe to grind here, and would like to know more about the song's history, too, but don't see anything new here.

For what it's worth, I'd always taken the titles in the song to refer to tunes rather than songs, and the words she sang each note... to mean that she sang along with the tunes, rather than sang them as songs.

Noreen