Season the chicken with salt and the cumin; transfer to a 6- to 8-quart slow cooker. Add the chipotle and adobo sauce, tomatoes and onion; toss to coat. Cover and cook on low, 6 hours.
Remove the chicken to a plate and set aside. Transfer the cooking liquid to a fat separator. Pour the liquid into a small saucepan, leaving any fat in the cup. (Alternatively, skim off the fat from the cooking liquid with a spoon.) Add the ketchup, 3 tablespoons brown sugar, 2 tablespoons cider vinegar and the Worcestershire sauce to the saucepan. Bring to a boil, then reduce the heat and gently simmer until the sauce is slightly thickened, 3 to 5 minutes.
Meanwhile, whisk 2 tablespoons vegetable oil and the remaining 2 tablespoons cider vinegar and 1 teaspoon brown sugar in a large bowl. Add the cabbage, radishes, scallions and ½ teaspoon salt; toss. Set aside.
Heat the remaining 2 tablespoons vegetable oil in a large nonstick skillet over high heat. Add the chicken and cook, stirring occasionally and pulling it apart with tongs or a fork, until browned and crisp in spots, 3 to 5 minutes. Stir in all but ½ cup of the sauce; season with salt.
Preheat the broiler. Slice the avocado. Put the roll bottoms on a baking sheet; top with the chicken and cheese. Broil until the cheese melts, about 2 minutes. Top with the slaw, avocado and roll tops. Serve with the remaining sauce.