Peel and devein shrimp. Cover and place in the refrigerator until they are needed.
Rinse shrimp shells and heads and place in a stock pot with 2 quarts of water. Bring to a boil, then reduce heat to a simmer and cook for 30-45 minutes to make a stock for the gumbo. Strain and discard heads and shells and reserve stock.
Wash crabs well and place them in a stock pot with 1 quart of water. Bring to a boil, then reduce heat to a simmer and cook for 20-30 minutes. Strain. Set crabs aside to cool and reserve crab stock. When crabs are cool, break off the two large claws and then break the bodies in half. Set these aside.
In a large, heavy-bottomed skillet, heat 2 tablespoons of cooking oil. Add okra and sauté over medium high heat for about 10-15 minutes. Make sure the okra is tender.
Add 2/3 cup oil to an 8-quart heavy-bottomed Dutch oven. Add flour and cook over medium high heat until a rich mahogany color (dark brown, but not black). Add onions, bell pepper, celery and garlic. Sauté, stirring occasionally, until vegetables are tender, but not mushy. You can allow the vegetables to stick to the pan slightly and scrape them off the bottom with a spatula or metal spoon to caramelize the vegetables well and bring out the most flavor.
Add tomatoes, bay leaves, black pepper, white pepper, and cayenne pepper, plus salt to taste. Cook 10 minutes, allowing everything to stick slightly and scraping it. Add cooked okra and cook 10 more minutes.
Add crab stock and half the shrimp stock. Stir constantly until the mixture comes to a boil. Then lower the heat to a simmer. Cover the pot partially (venting to let steam escape) and simmer 30 minutes, stirring occasionally. Use remaining shrimp stock to dilute the gumbo only if it seems to thick.
Add more salt to taste, if needed. Add the broken crabs and simmer for about 10 minutes. Then add the peeled, deveined shrimp. Bring back to a boil and cook until the shrimp are firm and pink, which should take about 5 minutes. Remove gumbo from the heat. Serve over steamed rice.