Aaaaahhh Joe, you beat me to it! Anyhoo, Rose of Tralee IS in the time loop:

Originally posted by IanC and nicked from THIS THREAD: "In the case of 'The Rose of Tralee', most authorities seem to agree that the lyrics are by C. Mordaunt Spencer, published in London in 1845 and the music is by Charles W. Glover."

[Me again]: I also heard somewhere that the background of this song was that Mary was a young girl the writer had been in love with but there was some obstacle to their marriage (that she was only a servant, I think) and by the time he'd sorted it out and he returned to claim her, she had died; so this Rose blooms only in memory. That's only hearsay (a.k.a. "the oral tradition"!) so it's open to correction or further clarification. Anyway, the period is right - it would certainly have been frequently heard in drawing rooms forty year later.

Another possibility is I Dreamt I Dwelt In Marble Halls, which is actually an opera aria (Dublin-born Michael Balfe, from The Bohemian Girl) - but it's sung here so often in informal settings, even now, that it's attained a similar status to Moore's melodies in the public imagination. Lovely song, slightly ambiguous if you don't know the story because you wonder if "you loved me still" is truth or just wishful thinking on the part of the singer. (In fact, she's singing about a real memory which she thinks is a dream, and all ends happily.)

Both in their differing ways are songs about loyalty and steadfastness of heart. Do please let us know what you decide upon - this thread is fascinating!