Position rack in bottom third of oven and preheat to 350 degrees F. Cook bacon in very large pot over medium-high heat until brown but not yet crispy, stirring often, 8 to 10 minutes. Add smoked suasuage, andouille, and tasso. Saute until meats start to brown in spots, about 10 minutes. Add onions, celery, and bell peppers. Cook until vegetables begin to soften, stirring occasionally, 10 to 12 minutes. Mix in chicken. Cook until outside of chicken turns white, stirring often, 5-6 minutes. Mix in paprika, thyme, chili powder, and 1/4 teaspoon cayenne. Cook 1 minute. Add diced tomatoes with chiles and broth; stir to blend well. Add more cayenne, if desired. Mix in rice.
Bring jambalaya to boil. Cover pot. Place in oven and bake until rice is tender and liquids are absorbed, 45-48 minutes. Uncover pot. Mix chopped green onions into jambalaya; spring jambalaya with chopped parsley and serve.
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