Uncle Jacque, the fact that Newton wrote the words tells us nothing about the music he used with them. In fact, I don't think I've ever seen anything discussing the tunes he used when first introducing these various words to his congregation. About all you can be sure of is that he'd use a tune they already knew & introduce words that fit is sermon topic.

You can find his original words at CCEL. This same tune & words can be found in Methodist Hymnals through the early 20th century. The tune name is different, but I'm pretty sure the current hymnal still has the tune but with different words.

Books like Missouri Harmony are well known for using folk tunes as the basis of the hymn tunes. I've always assumed it was a dance tune, just because it feels that way to me. Here's the version from the Southern Harmony. The tenor (melody) and treble parts are the same as those in the Sacred Harp. I don't know about the counter & bass.

A very common practice in these tunes is to have the tenor & treble lines sung by both men & women. These parts frequently cross. Just about everyone I know who has learned listening to a recording comes up with a tune that's a composite of the 2 parts. Even without a recording, I try to learn both treble & tenor parts & will frequently mix them up in my mind. So this type of thing could easily give rise to a 3rd tune.

Most of these old books had harmony parts that were in themselves pretty melodic. I think all 3 top lines of Southern Harmony's Green Fields look pretty melodic. I can imagine someone knowing the Harmony part for whatever reason & later using it as the tune for another song.