1. To prepare the stock, peel and devein shrimp, reserving shells. Cut each shrimp in half lengthwise; cover shrimp, and refrigerate.
2. Combine reserved shrimp shells, 8 cups water, and next 6 ingredients (through onion) in a large Dutch oven, and bring to a boil. Reduce heat, and simmer for 1 hour. Strain mixture through a sieve into a bowl; discard solids. Set aside 3 cups stock; keep warm. Reserve the remaining shrimp stock for another use.
3. To prepare the gumbo, heat a large cast-iron skillet over low heat; add 1/4 cup canola oil. Cook for 2 minutes, swirling to coat pan. Weigh or lightly spoon flour into a dry measuring cup. Gradually add flour to oil, stirring constantly with a whisk until smooth. Increase heat to medium; cook for 8 minutes or until the flour mixture is caramel-colored, stirring frequently. Cook 2 minutes or until mixture is chestnut-colored, stirring constantly. Remove from heat; slowly add warm shrimp stock, stirring until smooth. Pour stock mixture into a large bowl.
4. Heat 1 tablespoon oil in a large Dutch oven over medium heat. Add chicken; cook 7 minutes, turning to brown on all sides. Add onion and the next 5 ingredients (through bell pepper); sauté for 3 minutes. Return stock mixture to pan; add broth and bay leaves. Bring to a boil; reduce heat, and simmer for 45 minutes.
5. Add okra and next 3 ingredients (through black pepper). Simmer for 30 minutes.
6. Combine shrimp and paprika; toss to coat shrimp. Heat a large nonstick skillet over medium-high heat. Add remaining 1 tablespoon oil to pan; swirl to coat. Add shrimp; sauté for 2 minutes or until the shrimp are done. Stir shrimp into okra mixture. Discard bay leaves. Serve over rice.