Heat small amount of oil in heavy-bottomed pot, such as a Dutch Oven. Add the sausage and cook until browned, then remove. Quickly brown chicken and remove.
Add rest of oil and sprinkle the flour over the oil, add 2 tablespoons of butter and cook over medium heat, stirring constantly, to make the gumbo roux. Cook until brown (peanut butter colored), about 10 minutes (roux will appear chunky at first but it will thin out as it cooks). Adjust oil as needed to make roux. Let the roux cool (i.e. stop it from cooking further) by removing it from heat.
Add the remaining 3 tablespoons butter and the onion, garlic, green pepper and celery (this should cool roux) and return to heat and cook for 10 minutes. Add Worcestershire sauce, salt and pepper, to taste.
Add stock, chicken, sausage, thyme, paprika, and bay leaves, whisking constantly. Bring to a boil, then reduce the heat, cover, and simmer for 45 minutes. Add tomatoes, and okra; cover and simmer for an additional 1 hour.
Remove bay leaf and bunch of thyme. Add the green onions, shrimp, and chopped parsley.
Flavors intesify if refrigerated overnight.
Serve over rice.