Joe, hard to keep them straight.
1. The English Minstrel-Music Hall Billy Barlows- Billy is a raggedy comic commenting on English and European affairs. Not posted here yet.
2a. The American Minstrel Billy Barlows- the same raggedy comic but American-based material. Your # 2 and the (II) in the Trad. Index.
2b. The Australian Billy Barlows- He emigrates and gets taken. Not posted yet.
3. The homespun Billy Barlow, developed from 2a.- The Civil War Union patriot. My (3) and your second post above.
4. The American 'Hunting' Billy Barlow. In the DT and posted in 62969. Descended from old songs from Europe, certainly from "Fozie Mozie" posted in that thread, and possibly from the Cutty Wren song.
5. The outlaw Billy Barlow. Not in Mudcat as yet.

Note that I wrote Barlows- Several performers played the part, and each used somewhat different material.