While on the subject, there's a 48 page booklet by Charles Seeger: Versions and Variants of Barbara Allen, written to accomapny a Library of Congress record: Versions and Variants of Barbara Allen. He analyses the tunes for the song and the performances. There's a lot of information there on the tunes. You can download the pdf - link about half-way down the page. You can also download the songs (about 36Mb, link just after the pdf link). There are 30 versions; they vary in length from about 20 secs to 6 mins

He cites the Oswald tune as the first association of that tune variant with Barbara Allen.

Mick