Place bacon into a large Dutch oven over medium heat, and cook for 5 to 6 minutes, turning, until browned and crisp. Drain on paper towels; crumble pieces and reserve. Remove and reserve all but 2 tablespoons of pan drippings. Add sausage slices; saute for 3 to 4 minutes, stirring, until lightly browned. Remove to plate lined with paper towels. Meanwhile, toss chicken pieces with 1 teaspoon Cajun seasoning; add to pan along with ham cubes; saute until golden, for 3 to 4 minutes. Remove to plate with sausage slices. Add reserved bacon drippings to pan as needed. Stir onion, peppers, celery, and 1 teaspoon Cajun seasoning into pan; cook until vegetables are soft, for 3 to 4 minutes. Add rice and remaining 1 teaspoon Cajun seasoning; cook, stirring, until rice is translucent, for 3 to 4 minutes. Pour in broth, cover pan, and raise heat to medium-high. Cook until rice is soft, for 10 to 12 minutes. Stir in tomato sauce, 3 cups tomato juice, and hot sauce to taste; lower heat and simmer, uncovered, for 5 minutes. Add more tomato juice, if necessary; soup should be the consistency of heavy cream. Return cooked meats to pan and add shrimp. Cook, uncovered, just until meats are hot and shrimp is pink, for 4 to 5 minutes. Taste and adjust seasoning. Ladle into heated bowls. Serve garnished with reserved bacon crumbles and basil sprigs.