Bugsy: That's right ... I should have mentioned that in the last post. The "jolly" jumbuck is another figment of the Marie Cowan/Billy Tea rewrite.
McGrath: Paterson didn't do the re-write ... he had sold the rights totally ... and, in later years, was strangely silent about the poem. Before the Christina McPherson holograph material came to light, this was used to discredit Paterson and suggest he didn't write the poem. It now appears that the skeleton in his closet was his pitch for Christina (which led to the break-up of his seven years engagement to Sarah Riley, an old schoolchum of Christina's. Interestingly, the McPherson ladies remembered Paterson as "a bit of a cad"!
The actual content of the poem may well include oblique references to Bob McPherson's involvement in the swaggy's death ...and the cover-up, in his capacity as local magistrate. This is conjecture but interesting conjecture, especially when we see later hostile references to the McPherson name in Paterson's poems.
The Pete Coe rehash used the opening phrase and chorus, collected from the descendants of WW I veterans ... and their assumptions of a nice, acceptable "English" origin for the song. In fact, it arises from the tune of Robert tannahill's Scottish poem Thou Bonnie Wood of Craigielea, heard by Christina the year before, back home in Warnambool, Victoria.
GuestQ: The Australian National Dictionary (a full OED treatment of Australian words) give the origin of billy as from the Scottish dialect billy-pot - then cites your quote, from 1839 in New Zealand. This is followed by an 1849 citation for Australia. This usage is a typical preservation of a dialect term in a an ex-colonial country.