Combine 1 cup water, cumin, rind, 1 tablespoon oregano, and 6 garlic cloves in a small saucepan. Bring to a boil; remove from heat. Pour into a large bowl; cool to room temperature. Add remaining 6 cups water, salt, and sugar, stirring until salt and sugar dissolve. Stir in chiles. Pour salt mixture into a 2-gallon zip-top plastic bag. Add ice and pork; seal. Marinate in refrigerator 24 hours, turning occasionally.
Preheat oven to 450°.
Remove pork from bag; discard brine. Pat pork dry with paper towels. Combine juice, pepper, 1 teaspoon oregano, and 2 garlic cloves. Place pork in a roasting pan coated with cooking spray. Brush juice mixture over pork. Bake at 450° for 15 minutes. Reduce oven temperature to 325° (do not remove pork from oven); bake an additional 45 minutes or until thermometer inserted into thickest portion of pork registers 155°. Place pork on a platter. Cover with foil; let stand for 15 minutes. Thinly slice.