In a large bowl, combine 1/4 cup of the orange juice with the vinegar, olive oil, garlic, cayenne pepper, oregano, cumin, ancho chili powder, black pepper and 1 teaspoon of the salt to form a paste. Set aside.
Wash the pork shoulder and pat the meat dry with a paper towel.
Put the shoulder, fat side up, on a cutting board. Leaving the fat in a single piece and attached at 1 end, use a knife to remove the layer of fat from the shoulder, opening it like a book to reveal the meat. Then, use the knife to poke 1-inch deep holes into the meat on all sides. Rub the spice paste around the shoulder, working it into the punctures. Return the fat back to its original position. Score the fat with diagonal cuts and sprinkle the remaining salt over both sides of fat. Wrap the shoulder tightly in plastic wrap and refrigerate it for 8 hours or overnight.
Remove the pork from the refrigerator 1 hour before you start cooking.
Preheat the oven to 400 degrees F.
Pour the remaining orange juice into a roasting pan. Unwrap the pork from the plastic and put it in the pan, fat side up. Roast, uncovered, for 30 minutes, then lower the oven temperature to 300 degrees F. Roast for 3 hours and 45 minutes longer. If the orange juice dries up during the cooking process, add in more juice or water. Serve when the internal temperature of the pork reaches 185 degrees F on an instant-read thermometer. The meat should pull away with the prick of a fork and the skin is crispy. Remove the meat from the oven to a cutting board and let rest for 20 minutes, under a tent of aluminum foil, before serving. Slice the meat, arrange it on a serving platter and serve.