Place pork shoulder on a cutting board; using a sharp knife, score pork at 1-inch intervals. Place in a large, deep baking dish.

Combine coconut vinegar, garlic, 2 tablespoons salt, and black pepper in a blender. Process until smooth, about 30 seconds. Pour marinade over pork; cover and refrigerate 3 hours or up to overnight, turning once halfway through marinating.

Preheat oven to 325°F. Place guajillo chiles and 4 cups water in a small saucepan. Bring to a simmer over medium. Reduce heat to medium-low, and cook until chiles are tender, about 15 minutes. Drain chiles. Remove pork from marinade; set aside. Place marinade, chiles, ginger, tomato paste, coriander, cumin, sugar, bay leaves, and remaining 2 cups water in a blender. Process until smooth, about 60 seconds. Pour mixture through a fine wire-mesh strainer into a bowl, pressing to extract all liquid; discard solids.

Sprinkle pork with remaining 1 tablespoon salt, and place in an ovenproof Dutch oven. Pour chile mixture over pork; cover and roast in preheated oven until pork is tender and falling apart, about 4 hours. Remove from oven and uncover. (Cooking liquid should be the consistency of heavy cream. If too thick or scorching on the sides, add up to 1/2 cup water.) Increase oven temperature to broil on high with oven rack 12 inches from heat. Return pork to oven, and broil until pork is lightly browned on top, 5 to 10 minutes.

Remove pork from oven, and let stand until cool enough to handle, about 10 minutes. Remove meat from bone, and place in a large bowl. (If sauce isn’t thick enough, cook sauce over medium-high until thickened and slightly reduced to about 1 3/4 cups. Let stand 5 minutes.) Skim off and discard any fat from sauce. Pour 1 1/4 cups sauce over pork, and gently toss. Reserve remaining sauce.

Place about 1/3 cup pork on each tortilla, and top evenly with cabbage and radishes. Divide reserved sauce evenly among tortillas. Serve with refried beans.