If your slow cooker has an insert that can go on the stovetop, heat the oil in it over medium-high heat. (If it cannot go on the stove or you do not have a removable insert heat the oil in a very large (12-inch) non-stick skillet.) Once the oil is very hot, add the pork and chorizo in a single layer and cook, stirring until the meat has browned, about 6 to 8 minutes. Turn off the heat and place the insert into your slow cooker (if you’re using a skillet, transfer the meat and its juices into the slow cooker). Add the potatoes, onions, garlic, tomatoes with their liquid, chipotles, chipotle sauce, Worcestershire, oregano and 1/2 teaspoon salt and stir to mix thoroughly. Cook at the highest temperature.
The tinga will be finished after 6 hours at the highest temperature, though you can hold it for longer. (My slow-cooker can be programmed to switch from high after 6 hours to a keep-warm low temperature for up to another 6 hours. Some slow cookers click to keep-warm automatically; others need to be switched manually.)
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.