Boil carcass in enough water to cover until meat falls off the bones. Discard bones and strain duck stock.
Smother (cook slowly) okra by combining with 1 chopped white onion and 1 can of whole plum tomatoes. Cook in vegetable oil over medium-high heat until okra is soft and falling apart. Season with salt, black pepper and cayenne.
Season the duck meat with salt and pepper. Sear in a small amount of vegetable oil, over high heat in a large sauté pan until golden brown. Remove and reserve.
In the same pan, make a brown roux by combining vegetable oil and flour over medium-high heat while stirring constantly until the mixture becomes a dark reddish-brown.
Add remaining chopped white onion, celery, bell pepper, and garlic. Cook until wilted. Add very ripe tomatoes, reserved smothered okra, Andouille sausage, duck stock, seared duck meat, green onions, and parsley.
Simmer over low heat for 1 hour. Adjust seasoning with salt, pepper, and red pepper.
Cut duck skin into thin strips. Cook in a small pot to render the fat over low heat (approx. 30 minutes). Once rendered, increase heat and allow the skin to become brown and crisp.
Remove with a slotted spoon to absorbent towels. Season with salt and pepper, then reserve for garnish.
Add oysters 10 minutes before serving.
Adjust seasoning with salt, pepper, cayenne, and hot sauce.
Serve with cooked white rice, chopped parsley, and crisp duck skin as a garnish to each bowl.