In a large frying pan or Dutch oven, cook sausage in ½ tablespoon of oil over medium-high heat, turning, until lightly browned, about five minutes. With a slotted spoon, transfer sausage to a bowl.
Add remaining 1½ tablespoons oil to pan. Sprinkle chicken thigh and breast pieces with cayenne and fry in two batches, turning once or twice, until golden outside and white throughout, about 5 minutes per batch. Transfer to bowl with sausage.
Add celery, onions, and bell peppers to drippings in pan, reduce heat to medium, and cook, stirring often, until vegetables are softened, about 5 minutes. Add garlic, thyme, and marjoram and cook 1 to 2 minutes. Add rice and stir to coat grains with oil. Spoon vegetables and rice into shallow 3-quart baking dish. Cover with foil. (Recipe can be prepared a day ahead to this point. Refrigerate chicken-sausage mixture and rice and vegetable mixture separately. Return to room temperature before cooking.)
Preheat oven to 350°F. Stir broth and 1 cup of water into rice mixture. Cover with foil. Bake 35 minutes. Arrange chicken and sausage and drained tomatoes over rice. If rice seems dry, add up to ½ cup reserved tomato juice or water to the dish. Cover with foil and bake until heated through, about 15 minutes longer.
Season with salt, pepper, and Tabasco, stirring gently to mix. Sprinkle scallions on top. Serve directly from baking dish.