Closer to home than the Nevis songs from BWI are the black Creole songs and dances that developed in Louisiana from the late 18th through the 19th c. George W. Cable wrote about the creolized music in the 1880s (The Dance in Place Congo, Century Mag., vol. 31, issue 4, Feb 1886, pp. 517-532; "Old Creole Days," 1879, 215pp., Scribners; and others). The French language, the influence of the Catholic church, and French musical forms were imposed on basic African rhythms and new forms evolved.
At the same time, Lafcadio Hearne was describing Creole life in Martinique; although far afield from your suggested thesis, New Orleans traders were active in the French West Indies. Hearn and H. E. Krehbiel transcribed some of the songs.

The influence of this Black Creole music and dance on early New Orleans jazz has yet to be studied in any detail. Counjaille, Calinda and other lyrics were sung and danced, mostly to percussion instruments, but at the same time there were black Creoles, free and slave, who were proficient on stringed and band instruments.