Heat the olive oil in a saucepan over medium-high heat. Stir in the onion, garlic, and ginger, and cook until tender. Reduce heat to low. Mix in ketchup, brown sugar, molasses, rum, hoisin sauce, tomato paste, vinegar, chili powder, and cayenne pepper. Cook and stir 5 minutes, until well blended and heated through. Stir in remaining rum.