See the thread Lyr Req: Amazing Grace 'disrobed' stanza for a fair amount of discussion about this style of singing. See especially Jean Ritchie's discription of her mother's church.

I've looked at a couple of books, and am reminded that the black churches that sing in this style often called it "Dr. Watts singing" even if Watts had nothing to do with it.

I have a 1906 word book published by a Baptist group shortly after published a hymn & tune book. It describes the hymns as "old meter hymns" and "old meter songs." It was to satify the demand for "the old style pocket edition, as each member desired to have his or her own pocket hymn book, and select and sing the old meter songs of his or her choice

Wilco, if you're in eastern TN, it seems like you might be able to find some churches nearby that sing this way.