I have to agree with the notion that the Monroe Doctrine would have been invoked with respect to Cuba. Now, presuming the timing originally mentioned is approximately correct, this sort of implies a war in the late 1880s; i.e., during Benjamin Harrison's tenure (and thus a war while TR was just beginning to enter politics/had returned from the Dakotas). I could see thus TR as a captain in a regiment of volunteers from the New York metropolitan area, or perhaps as a lieutenant in the US Navy. But what boggles my mind is the possiblity of the Human Iceberg (i.e., Harrison) somehow gaining sufficient popularity to win a second term.