Mix vinegar, brown sugar, molasses, honey, Worcestershire sauce, rum, mustard, liquid smoke, ground chile, black pepper, garlic powder, and allspice together in a heavy saucepan over medium heat. Bring to a boil, reduce heat, and simmer until sauce is smooth and brown sugar is dissolved, about 5 minutes.
Stir ketchup into sauce and bring to a boil. Reduce heat and simmer, stirring occasionally, until sauce is dark and thickened, about 30 minutes.
