Season pork cubes with salt, pepper, and thyme to taste and place in a cast iron skillet.
Cook pork cubes in the preheated oven until cooked through, about 30 minutes. Transfer pork from skillet to a bowl, reserving drippings.
Cook and stir bacon in a 9-quart Dutch oven or heavy pot over medium heat until browned, 5 to 7 minutes. Remove bacon with a slotted spoon and place on a paper towel-lined plate, reserving bacon grease.
Cook and stir okra in the bacon grease over medium heat until lightly browned, about 5 minutes. Transfer okra to a bowl, reserving bacon grease. Cook and stir smoked sausage in bacon grease until browned, about 5 minutes. Add onion, bell pepper, celery, and garlic to sausage; cook and stir until softened, 5 to 10 minutes.
Stir 48 fluid ounces chicken stock into sausage mixture and bring to a simmer. Stir roux into broth mixture until dissolved and slightly thickened, 2 to 3 minutes. Slowly stir 48 fluid ounces chicken stock into thickened stock; bring back to a simmer.
Mix pork, pork drippings, bacon, chili powder, paprika, 2 teaspoons black pepper, file powder, rosemary, 1 teaspoon thyme, bay leaves, and Creole seasoning into thickened chicken stock; simmer, stirring often and skimming off fat, until flavors blend, about 1 hour.
Stir black-eyed peas, mustard greens, okra, diced tomatoes with green chile peppers, mushrooms, and remaining chicken stock into pork-stock mixture; simmer for 1 hour more.