To make the marinade, mix spices and sugar together in one bowl and lime juice, zest, soy sauce and oil in another. Combine wet and dry ingredients into one bowl. Set aside.
Preheat oven to 300°. Place the rack of ribs on a large sheet tray or cutting board. Remove the membrane from the underside of the ribs with a small knife and a paper towel to grip the membrane. Place ribs on large sheet of aluminum foil on a baking tray. Rub marinade all over ribs and wrap completely with foil. Place in oven and bake approximately two hours or until rib temperature is 195˚ to 200˚. Remove ribs from oven and turn oven to broil. Remove foil from ribs and brush both sides with barbecue sauce. Leaving the ribs uncovered, broil until sauce just starts to caramelize, 2-3 minutes. Pull ribs from oven and transfer to a cutting board. Cut into pieces and serve.