I'd think it more likely that an American variant of the Wren hunting song acquired Barlow from the stage songs. The examples referred to by the TBI overlap to an extent. The Lomax and Seeger songs are from the same source, and Barlow is not mentioned in the Brown example; are the others separate, and do they name him? So far as I know, he appears in no British or Irish variants at all. As I mentioned in the other thread, the closest Barlow gets to the song in the Old World is the first line of the broadside: Oh when was I born, says old mother Goose. Not very near.

Now, then. A "Civil War song by Edward Clifford". I wonder if that's the one at the Midi Pages? It is sub-titled "a Civil War song", and bears an uncanny resemblance to sheet music for Billy Barlow at Levy. Completely the wrong tune then, it appears, and nothing at all to do with our "Wren" variant here...