Combine beef roast, tequila, jalapeno peppers, and garlic in a slow cooker. Cover and cook on Low until tender, 12 to 18 hours.
Shred beef using 2 forks; let it cool, about 30 minutes. Transfer shredded beef to a plate using a slotted spoon, reserving cooking liquid in the slow cooker.
Pour reserved cooking liquid into a large pot; stir in rice. Bring to a boil. Reduce heat to medium-low, cover, and simmer until rice is tender and liquid has been absorbed, 20 to 25 minutes.
Preheat oven to 350 degrees F (175 degrees C).
Mix black beans, refried beans, and 1 can green chile peppers together in a bowl.
Mix spicy enchilada sauce, mild enchilada sauce, and tomato paste together in a bowl until smooth. Spread a thin layer of sauce in the bottom of a deep baking dish.
Spoon 1/4 cup bean mixture, 1/4 cup rice, 1/2 cup shredded beef, 1 tablespoon sauce, and 2 tablespoons Mexican cheese blend over 1 tortilla. Roll up tortilla and place seam side-down in the baking dish. Repeat with remaining ingredients until baking pan is full.
Cover tortillas with a thick layer of sauce and remaining cheese. Spread remaining 1 can green chile peppers over cheese.
Bake in the preheated oven until cheese is bubby and golden brown, 45 minutes to 1 hour.