The Encyclopedia of Arkansas (perhaps predictably) has a good description of the song's history, though as your above reference makes clear their dates are later than it seems is actually the case.

The earliest printed text of this song may be that which E. C. Perrow published in Journal of American Folklore in 1913. The earliest sound recording is probably the one by Kelly Harrell and the Virginia String Band, done in a studio in Camden, New Jersey, in 1927. One of Vance Randolph’s Ozark consultants, however, suggested that he knew the song from the 1890s. Writing in Arkansas Historical Quarterly, Robert Morris proposed an earlier origin date, in the 1870s. Several commentators, including Library of Congress folksong researcher Alan Lomax, hypothesized that the song was of Irish-American origin. It does bear some resemblance to “The Spalpeen’s Complaint to the Cranbally Farmer,” which Patrick Weston Joyce published in 1909. Ballad scholar D. K. Wilgus reported a text of the song from Ireland and proposed that it had originated there and was imported to the United States in the late nineteenth century.

When G. Malcolm Laws created his catalogue of what he called “native American ballads,” he included “The State of Arkansaw” as the first entry in his chapter “Ballads on Various Topics.” He also contributed to some confusion about the song by titling it “The Arkansas Traveler.” Though it has been reported under that name—along with “The Arkansas Navvy,” “A Hobo in Arkansas,” and “The Arkansas Emigrant,” among others—“The State of Arkansaw” has no connection with the skit and fiddle tune to which Laws’s title usually refers. It more likely derives from the tradition of complaint songs popular in the nineteenth century, which responded to the failure of westward migration to meet media-generated expectations. “The State of Arkansaw” joins “Michigan-I-O,” “The Dreary Black Hills,” “Nebraska Land,” and “The Lane County Bachelor” in a category of “folk dystopias,” hyperbolic descriptions of frontier disappointments.

Fresno State writes the earliest known date was 1906.