I have the first lp and the cd of that 1975 version and the cd of the 1993 version with Tom Waits. The liner notes probably just echo what Bryars has said elsewhere, the film project of his friend, the tramp, a religious man who was not an alcoholic, as most if not all of the other taped tramp voices were, how he came to put music to it, the various public performances and then the definitive version scored in 1974, recorded and released in 1975. The 1993 liner notes say that the later variations were inspired by Tom Waits looking for another copy of the 1975 lp, trlling Bryars it was his favorite recording, etc., so Bryars was inspired to add Tom Waits' voice to another version. Both versions are hauntingly beautiful, no matter what you religious persuasions. I have a really hard time reconciling my feelings about the lyrics, which are negative, and the emotion that the tramps singing and Bryars orchestration engenders. I try not to think too much about it and just let myself be swept away in the music, without ever being convinced that Jesus' blood has ever done anything as constructive as the further bloodshed it has caused has created such great human sufffering in the world. The tramp, I feel was inspired by his own faith to create his own sung witness, if it gave him any ease and comfort, which I'm sure it must have, that is ok by me, I can't agree with his sentiment but I accept it as real for him. I doubt very much that you will find any earlier source, and there needn't be one, trying to parse it as based on 'Jesus Loves Me' or any other hymn is unnecessary and futile. The tramp is the sole source, how it came to him we won't know, since Bryars says he died before the work was complete, and he never identifies him by name, if he knew the tramps name, though they might have had a release signed by him?
I have myself tried substituting lyrics of my own, Jesus' Love doesn't mean anything more to me than Jesus' Blood, though nothing else has the same emotional weight as the original to my ears. I go long periods without listening to it, and then have to hear it over and over again for a spell.

Bryars 'The Sinking of the Titanic' is also beautifully powerful and worth listening to. Many questions raised by that one as well, and all the possible melodies that the band on the Titanic might have been playing as it went gown are incorporated into Bryar's piece: Autumn, (both ragtime tune and hymn), Aughton, and Nearer my God to Thee. Tape loops of voices from the survivors and subsurface sounds of the ship on the bottom add to the instrumentation and create quite a sublime listening experience.