Heat the oil in a stovetop-rated slow cooker liner over medium-high heat. (If your slow cooker liner isn’t made from a material that can be used on a stovetop, use a very large (12-inch) non-stick skillet.) Once the oil is very hot, add the pork and chorizo in an single layer and cook, stirring until the meat has browned, about 6 to 8 minutes. Turn off the heat and if you’re using a skillet, transfer the meat and its juices into the slow cooker. Add the potatoes.
In a large bowl, combine the onions, garlic, tomatoes, chipotles, adobo sauce, Worcestershire, oregano and 1/2 teaspoon salt. Pour mixture into the slow cooker and stir to mix thoroughly. Cook for 6 hours at the highest temperature.
After six hours, gently stir the tinga. If the sauce seems too thick, stir in a little water. Taste, and season with salt if you think the dish needs it. Scoop into a large bowl, sprinkle with the fresh cheese and diced avocado, and serve with warm tortillas.