Perhaps you have already picked it up, but the recent Smithsonian Folkways release,"If I Had My Way: Early Home Recordings--Rev. Gary Davis", SFW CD 40123, includes in its notes commentary on the various songs by Horace Boyer, an expert on the gospel tradition, who talks about sources and precursors of the various songs Rev. Davis performs on the CD. It strikes me that his commentary might save you some work or at least point you in the right direction.
All best,
Johnm
Perhaps I may suggest as a complemetary CD to the above, Shanachie's :Demons and Angels: Rev. Gary Davis: The Ultimate Collection". It was released in 2000 so may be deleted for all I know, but what I do know is that one of the motivating forces behind it was modest Frankie, so...