This is already in DT twice: Here and Here, from the singing of Sarah Ogan Gunning. It's on Folk Legacy FSA 26, so Sandy may have more info. MMario is still looking for the tune.

Your title made me think of Desire for Piety in the Sacred Harp. "Then I'm going home" really sounds like it should be Sacred Harp, but it's not.

I'd suspect it has its roots in Camp or Revival Meetings. The Chorus really having very little relation to the verses & probably having floated around being independently attached to any number of verses is pretty characteristic. I see it's on Ginny's album for her father, but the verses don't seem Primitive Baptist to me.