No. 1860 is correct. Moore (1828-1904) was a journalist and a diligent collector of newspaper stories, popular poetry, etc. He compiled the multi-volume "Rebellion Record" during the Civil War.
The phrase "oral tradition" was probably unknown to him.
The English-born John Anthony Scott (1916-2010) produced several books on American history for teenagers. There's no doubt that "Polly Wand" was his own contribution. If Scott's text cannot be traced to an earlier publication, only one conclusion can fairly be drawn.
It sounds to me as though Paul Clayton's text is the one that resembles the printing by Coverley. The album notes suggest that Clayton's lyrics come from either Leach's "Ballad Book" or else from Philips Barry's 1935 monograph on the song - at least according to the album's notes.