Combine 1 teaspoon salt, paprika, and pepper. Trim fat from pork. Cut pork into 2-inch pieces; trim any additional fat. Combine pork and paprika mixture, tossing well to coat.
Heat a large Dutch oven over medium-high heat. Add pork; cook 5 minutes, browning on all sides. Remove pork from pan. Add onion and garlic to pan; sauté 3 minutes. Return pork to pan; stir in water and next 7 ingredients (water through chicken broth).
Remove 1 large chile and 2 tablespoons adobo sauce from can; reserve remaining chiles and sauce for another use. Remove seeds from chile; finely chop. Stir chile and adobo sauce into pork mixture. Bring to a boil; cover, reduce heat, and simmer 2 hours or until pork is tender. Remove pork from pan using a slotted spoon; place pork in a large bowl. Shred pork using 2 forks. Add tomato mixture to pork in bowl. Let cool to room temperature; cover and chill overnight.
Skim solidified fat from surface of stew. Combine the stew, remaining 1/2 teaspoon salt, and hominy in a large Dutch oven, and bring to a boil over medium-high heat. Reduce heat; simmer 5 minutes. Ladle 1 cup stew into each of 10 bowls; top each with about 2 tablespoons of lettuce, about 1 tablespoon of chips, about 1 tablespoon of cilantro, and about 1 tablespoon of radishes.