Preheat the oven to 325°F.
In a large bowl, combine the salt, onion powder, garlic powder, paprika, pepper, cayenne, ginger, and dry mustard. Add the short ribs and rub in the spice mixture until the meat is well coated on all sides.
Heat 5 tablespoons of the canola oil in a Dutch oven or large heavy-bottomed ovenproof pot over medium-high heat. Sear the short ribs, in batches, on both sides until nicely browned, about 4 minutes per side. Remove the meat from the pot. Add the remaining 1 tablespoon oil, the onions, and the garlic and sauté until caramelized, 8 to 10 minutes. Return the short ribs to the pot. Cover with the barbecue sauce, 2 cups water, and the Worcestershire and bring to a boil. Cover the pot and transfer it to the oven. Cook until the meat is falling off the bone, about 4 hours.
Remove the meat from the pot and place it in a large bowl. Discard the bones. Shred the meat into small pieces using two forks. Use a ladle or large spoon to skim the fat from the sauce. Add enough of the sauce to the meat to moisten it well (reserve the rest of the sauce for another use if you like).
To assemble the sandwiches, open up the burger buns, and and spread each side with 1 tablespoon mayonnaise. Top with 1 cup meat and one-quarter of the avocado slices.