See if you can find this book in a library. I've never looked at it very closely. I'd suggest you view it as a source for songs that are related & perhaps not so strongly for which came first.

Jackson, George Pullen, 1874-1953.
White and Negro spirituals, their life span and kinship, tracing 200 years of untrammeled song making and singing among our country folk, with 116 songs as sung by both races,
New York, J. J. Augustin [1944]
xiii, 349 p. incl. front., illus. (incl. ports., music) 24 cm.