Preheat oven to 425°F (218°C). Remove the giblets and wash the duck well. Split it down the backbone with either shears or a sharp boning knife. Flatten it slightly by cracking the ribs and pressing down on the septum. Sprinkle with salt and pepper and place it skin side up on a rack above a roasting pan or baking sheet (with sides to contain the grease). Poke the skin all over in the fatty areas to yield excess fat while cooking and roast for about 1 hour on the upper level of the oven or until juices run clear from the thigh. If unsure, err on the side of undercooking.
While duck is roasting continue with other preparations. Slice the sausage and dice the ham and giblets, setting aside for later use.
Chop the peppers, celery, onions, and garlic. Melt the 3 tablespoons of fat in the Dutch oven and sauté the vegetables over low heat until tender. Reserve in a bowl.
Drain the tomatoes, reserving the juice, and chop them. Combine them with the juice, chicken stock (or water), salt, pepper, Tabasco, basil, thyme, and bay in a saucepan and simmer for 20 minutes.
Sauté the rice in the 2 tablespoons of fat in the Dutch oven until just barely browned. Do not overcook or allow to pop. Reserve in a bowl.
When duck is done, remove to cool. Using 3 tablespoons of rendered duck fat from the pan, brown the sausage, ham, and giblets in the Dutch oven. Remove with a slotted spoon and reserve.
Carefully remove excess grease from the roasting pan, taking care to leave behind any rendered juice or browned bits from the duck. Add these to the tomato mixture. When the duck is cool enough to handle, remove all meat from the bones (with skin intact) and chop it roughly.
Preheat the oven to 350°F (177°C). You are now ready to assemble the Jambalaya.
Scatter the sautéed vegetables over the bottom of the Dutch oven. Add the browned rice, distributing it evenly. Next add the meats: sausage slices, giblets, ham, and duck. Over all pour the hot tomato mixture. Cover tightly with a lid (or aluminum foil) and bake for 1 hour. The liquid should be absorbed and the rice thoroughly cooked.