Peel and devein shrimp. Place shrimp into a bowl; cover and refrigerate until needed. Place shrimp heads and shells into a large pot.

Pour 2 quarts water into the pot, cover, and simmer over medium-low heat until liquid is reduced by half. Strain out and discard shrimp heads and shells. Reserve shrimp broth.

Heat oil in a very large stockpot over medium-high heat. Add flour; cook and stir with a long-handled spoon until dark brown and flour puffs and starts to absorb oil, 10 to 15 minutes.

Slowly stir in chicken broth and 1 cup water. Place chicken into the pot; add tomatoes, onions, celery, bell pepper, garlic, seafood seasoning, salt, cayenne pepper, and bay leaves. Bring to a boil and cook until chicken is no longer pink at the bone and the juices run clear, about 1 1/2 hours.

Remove chicken from the pot and set aside until cool enough to handle. Remove and discard bones; chop meat into 1-inch pieces.

Return chopped chicken to the pot, along with reserved shrimp broth, crabmeat, sausage, shrimp, and filé powder; stir from the bottom of the pot to combine. Bring to a boil, then immediately remove from the heat.