Looking at the Billy Barlow-Hunting song in the DT, The Lomax (FSNA) entry, and the citation for Brown, the earliest of these is is in Brown, 1916 (titled "Let's Go A-Hunting"). Is there proof of an earlier date of collection? My guess is that it is mid- to late 19th c, but a guess only. How early have you found it, Joybell?

Use of the name 'Billy Barlow' in the title seems inappropriate, since 'BB' in the verses is just one of the four. The title in Brown, (NC Folklore) and the Lomax title in FSNA, "Let's Go A-Huntin'," seems more appropriate than the title "Billy Barlow" applied by the Lomaxes in "Our Singing Country." Were they the first to title this version "Billy Barlow"?

I tend to agree that the name Billy Barlow was just slotted in, perhaps by some performer who was familiar with the very popular Cowell (and others) routines. Cowell was famous, but many performers built on his routines; there is no reason (unless Joybell has found something) to associate him with this version, which was collected in an east coast state (Brown).
I would guess some unknown (so far) American performer (agreeing, apparently, with Joybell).
The Lomaxes make no mention of Brown and his prior collection of the version they obtained from a Bud Wiley, Zweiful Ranch, Texas, in 1935.