A couplet from the ballad dates to 1907 or so (could be 1909), then came Perrow's version (1912) and versions collected by Lomax (ca 1912) and Combs (published much later). One stanza appears in the Atlanta Constitution in 1913.
The ballad was probably written shortly after the event that inspired it, so it dates to 1871 or 1887 if we accept Big Bend, Lewis, and Oak/Coosa Tunnels as the candidates. If 1887, then 20 years passed before anyone noticed it in print (as far as we know). If 1871, then 36 years. Obviously, the chance that 20 years would pass without such notice is greater than the chance for 36 years.
It is especially noteworthy that there is no notice of John Henry in print between 1871 and 1887.
There are several pieces of statistical evidence that favor 1887 weakly. An accumulation of pieces of weak evidence is stronger than one isolated piece.