"Can the Circle be Unbroken?" was included in Randolph, "Ozark Folksongs," vol. 4, no. 635, coll. 1941. The verses are the same as those used by the Carters in their recording, and that probably was the source. A line or two of the Carter song could come from earlier songs, but the verses are not in the pre-1935 literature I have seen.

I would like to see the text of the Welling-McGhee recording, if available.

The song was used many times on the Nashville Grand Old Opry, in the upbeat form initiated by the Carters.
The verses of the Habershon hymn are very different, only the refrain is retained, and the midi of the C. H. Gabriel music at Cyberhymnal is dolorous and slower. I have not seen sheet music by Gabriel, or heard his music in his original form.