Does C.L. Lofthouse music qualify as originating in the West Indies? Certainly not by any visiting folklorist-musicologist's metric.
However the Lofthouse family name in the Bahamas goes back before the American Civil War. Charles Leonard Lofthouse was born in Nassau in 1883 to the Rev. T.H.C. Lofthouse and the former Elizabeth A. Menendez. Graduated Queen's College, NP with voice and piano in Paris. The Lofthouse Record Company was putting out 78s before World War II. The Lofthouse Agency was making goombay flexi-disks in the late 1960s.
I think the "The Winds of Dawn" (1911, music, w/ lyric by Julia Warner Michael) was Charles Lofthouse's first published song, after the preceding year's "Modern Singing Lesson" monograph. He was 29 years old at the time. It and several others were already moldy-oldies when he was pulling strings (literally and figuratively) in the 1930-1950 pop-goombay "discovered" by the Americans. Whiteman's Rhythm Boys (post Crosby) did this tune and Lofthouse-Gilbert's "Bahama Mama" (1932.)