We didn't find any Playford tunes with "Patrick" in the title either--we suspected that the tune Petrie refers to in Playford has a different name. From what I've managed to listen to in abc formats, and by comparing music notation, "Never Love Thee More" seems to be very similar--ie musical phrases that match.
Bruce, I think this case might be similar to that of the "original" melody you and Mr. Robinson found for "Londonderry Air"--have to listen closely to hear the similar musical phrases, though "Never Love Thee More" seems more evident to me...especially when you slow down the tempos.
What is your opinion on the melody comparison of the two tunes (Never Love Thee More and St. Patrick's Day), Bruce? Feel free to email me if it is easier.
Mary SingsIrish@email.msn.com