EJ, I echo Masato's recommendation of Dena J. Epstein, "Sinful Tunes and Spirituals, Black Folk Music to the Civil War." It is the only solid study that is readily available. Amazon has new copies for $38.66 but also list used copies for about $19. Abebooks lists 22 used copies for sale.
Also check Epstein's "African Music in British and French America," and the "Folk Banjo," both out of print, but available used and in libraries.

That spiritual songs were sung, along with secular, was noted by Frederick Douglass. "A silent slave is not liked by masters or overseers." An ex-slave reported "we had a jackleg slave preacher who's hist the tunes. Some was spirituals." Epstein, p. 162.
Epstein reports the presence of slaves at camp meetings (Noted by a Bishop Asbury in 1801 and succeeding accounts). Of course practices varied across the South.

For Alabama, try to get Hobson, Anne, 1903, "In Old Alabama, Being the Chronicles of Miss Mouse, the Little Black Merchant," Doubleday, Page, NY." This book, which Epstein says was of Uncle Remus type, neverless reported dances and songs that have been corroborated by other sources.

"The Old Ship of Zion" is one of the first recorded spirituals, in call and response form, 1850s lyrics recorded. Unfortunately, although observers reported the singing and the religious services, thay did not record the songs.
"Carry Me to the Burying Ground" also recorded.
"Brothers Walking to the New Jerusalem" may have come from the camp meetings.
Epstein reprints a few more. One might find more in the references that she cites.

The spirituals in Allen and Fenner, from the period of the Civil War and the succeeding decade, may be influenced by the spirituals of free blacks, since black and slave became associated in the institutions where they collected the songs.