It was not until some time later that I spotted a small sea bird heading past us the opposite direction. I was able to get the binocs on it and saw a dark brown bird with a bold white rump and brown/ white undersides. When I consulted my Collin's Gude to Birds if the West Indies, I immediately suspected Jamaican Petrel! Unfortunately further reading indicated that the bird is most likely extinct... So my only other possibilities are Wison's, Leach's, or Band-rumpled Storm Petrels, with the latter most possible based on flight behavior (steady, not erratic, and purposeful). For now it'll just remain "some bird".