Rinse the fish in cold water and pat dry with paper towels. Brush both sides with marinade and lay on a plate (or on a broiler rack or baking sheet if broiling); set aside. Preheat a charcoal grill or broiler.
Add enough chicken broth to the reserved pineapple juice to measure 2 cups. Stir the broth mixture, pineapple, rice, bell pepper and allspice together in a medium saucepan and bring to a boil over high heat. Cover, reduce the heat to low and simmer until the liquid is absorbed, 18 to 20 minutes (or cook in a rice steamer). Take from the heat and let stand until ready to serve; discard the allspice berries.
When the rice has cooked 12 to 15 minutes, place the fish on a lightly oiled grill and cook 3 minutes. Turn over and cook until the fish is just barely opaque but still moist in the center, 2 to 3 minutes more for 3/4-inch-thick steaks (or broil, without turning, for 6 to 8 minutes).
Fluff the rice with a fork, stir in the green onions and spoon onto
individual plates. Transfer the swordfish to the plates and garnish with lime wedges.