Rome County -Harrison Burnett, Fayetteville, Arkansas. July 11, 1958 Hills Of Rome County -Harrison Burnett, Fayetteville, Arkansas. July 5, 1960
The Roud Folk Song Index lists Roane County at number 3387, and Precious Jewel at number 18658. There are no entries at present that would take the date back much beyond the 1940s.
I may be able to look up the Kirkeminde article in Tennessee Folklore Society Bulletin, but apparently Sheffield only has microfilm of a "damaged set" of that publication, so don't hold your breath.