In the book the song is written out in 4-part harmony. The notes say:

"Tune and st. 1-4 from DES [Down-East Spirituals, by George Pullen Jackson, J. J. Augustin, New York, 1941] p. 26, quoted from a MS 4-shape song book made near Emmitsburg, Md., between 1800 and 1839; st. 5 and accompaniment from Repository of Sacred Music, Part Second, by John Wyeth, Harrisburg, Pa., 1820, p.29."

Although undoubtedly inspired by the book's setting, given that Mike & Peggy's performance is 2-part, getting their version of the harmony from the recording is probably your only option.

~ Becky in Tucson