Listening to the Blind Willie Johnson recording again, I think I can hear the hymn tune (RICHMOND) underneath it, but maybe I'm imagining. Johnson's recording is certainly tied to the two versions on the Folkways link. The recordings on the Scott Sandvik link are of the same style (I couldn't find Sandvik's recording of "Dark" online).
My question is, what do you call this style? Is this what you call a "moan"?
It's very similar to what the congregation sings in hymn-lining, quite far removed from the standard tune for the hymn.

-Joe-