Warm the bacon drippings in a large, heavy saucepan or stockpot over medium heat. Add the pork, onions, and garlic and sauté until the meat is lightly browned, about 10 minutes. Add the posole, stock, oregano, salt, bay leaves, and thyme and bring the mixture to a boil. Reduce the heat to medium-low and simmer, uncovered, for 1 hour. Add the chiles and continue simmering for another 1 to 1½ hours, or until the corn is puffed and tender but still a little chewy. Add more stock if necessary to keep the mixture rather soupy.

Keep the posole warm for up to 1 hour, and serve ladled into bowls garnished with limes, green onions, cilantro, and radish.