Slit chiles lengthwise, then stem and seed (leave veins for heat). Heat a dry large heavy skillet (not nonstick) over medium heat until hot, then toast chiles in batches, opened flat, turning and pressing with tongs, until more pliable and slightly changed in color, about 30 seconds per batch.
Transfer chiles to a bowl and soak in hot water until softened, 20 to 30 minutes. Cut a shallow X in bottom of each tomato and blanch in simmering water 20 seconds. Transfer with a slotted spoon to an ice bath to stop cooking. Peel tomatoes. Coarsely chop, reserving juice.
Preheat oven to 350°F with rack in middle. Cut goat at joints to separate into pieces and put in a 3-quart shallow baking dish. Sprinkle all over with 1 1/2 teaspoons salt.
Drain chiles, discarding soaking water, and purée in a blender with tomatoes and reserved juice, 3/4 teaspoon salt, and remaining ingredients except tortillas until very smooth, about 1 minute.
Pour sauce over meat, turning to coat, then cover dish tightly with a double layer of foil and braise in oven until meat is very tender, 3 to 1/2 hours. Remove from oven and cool meat in liquid, uncovered, 30 minutes. Preheat oven to 350°F.
Coarsely shred meat, discarding bones, then mix into braising liquid in dish. Return to oven and cook, covered, until sauce is simmering, about 30 minutes more. Fifteen minutes before goat is done, make 2 stacks of tortillas and wrap each stack in foil, then heat in oven on rack alongside baking dish. Serve goat with warm tortillas and accompaniments.