Journal of American Folklore vol 24 (1911), in an article on "Negro Folk-Song and Folk-Poetry", has this lyric in the song "Take Your Time":

Tain't but the one thing grieve my mind:
Goin' away, babe, an' leave you behin'

http://books.google.com/books?id=7zedAAAAMAAJ&pg=PA274&dq=gwine+%22grieve+my+min

Context: The idea I'm advancing by quoting these lyrics is that the lyrical style of "South Australia" matches the style of African-American folk songs AND/OR American minstrel songs. Like many chanties, I think South Australia is cut from that cloth, so it's possible that the elusive "Rolling King" will be found in the language of that cultural context rather than, say, in anything Australian. "Rolling King" may have originated as a chorus before the Australia-specific theme was created.