A more reliable source than the AllMusic site I referenced previously, AirPlay Direct, has virtually the same credit for Jones' An American Original album, crediting both Alton Delmore and Grandpa Jones. Based on that, I found the BMI listing, which is:
DARBY S RAM Writer / Composer: DELMORE ALTON, JONES LOUIS M Publishers: FORT KNOX MUSIC INC (BMI), TRIO MUSIC COMPANY (BMI), VIDOR PUBLICATIONS INC (BMI) BMI Work ID: 277939, ASCAP Work ID: 890312792 ISWC: T9196513312
This is where things get a bit strange, though: the US copyright office doesn't have an entry I can find prior to a mass entry of material in 1983 by Ft. Knox (document V2011 P243-948). I'd initially assumed that the Delmore/Jones copyright was only meant to be (retroactively) applied to the 1948 King release, but Jones' 1981 album Family Gathering also credits both Jones and Delmore -- before the 1983 copyright date. Adding to the confusion, Jones' 1963 release Rollin' Along With Grandpa Jones (where the recording I started this thread with originated from) credited the song as "Traditional - P[ublic] D[omain]." The Delmore/Jones credits didn't appear alongside that recording until the same song was later re-released on compilation discs; the 1998 An American Original is the first I can find.
After all that, I'm inclined to think that the 1983 submission was a renewal -- at the time, musical works were on a 28-year cycle, which would suggest an initial execution of 1955. However, I haven't found anything in that era, or earlier (when the 1948 King release came out), and I spent much more time than I should have perusing the Copyright Catalogs, both the book forms on archive.org, and the (very janky) digital card catalog.
Good work on finding the Skyland Scotty version -- I hadn't heard that one. Definitely seems like Jones may have 'borrowed' it from him (or perhaps both borrowed it from another source!). The 1948 Delmore/Jones recording hints Grandpa "used to sing it all the time," but I can find no references to him performing it prior to that disc's release.