Just had a closer look at Bronson. In his notes to var 40 (the Johnson tune) he adds: "The tune may make an earlier appearance in Oswald's A Curious Collection of Scots Tunes [1740], p3, and in his Caledonian Pocket Companion II (ca1745), p27, which I have been unable to compare" (my bold).

So it appears he was just unable to verify these tunes.

I couldn't find a copy of A Curious Collection of Scots Tunes online (at a quick look), but assuming Bronson is correct, this pushes the date back to 1740.

Jack Campin certainly has some tunes from A Curious Collection, so maybe he can verify the Barbara Allan tune. (I'll try and look through his site, but I'll contact him - it may be quicker!).

Mick