Heat the oven to 375°F (190°C). Place the guajillo chiles in a heatproof bowl, cover with the boiling water, and let them soften for 10 minutes. Drain the chiles, reserving none of the soaking water.
Add the softened chiles, tomatoes and their juices, roughly chopped onion, garlic, chicken broth, Mexican oregano, and salt to a blender. Blend until completely smooth. Take care when blending warm ingredients: vent the blender lid according to the manufacturer’s directions.
Heat 1 tablespoon oil in a medium saucepan over medium heat. Carefully pour in the blended sauce and simmer, stirring occasionally, until slightly thickened and glossy, about 10 minutes. Taste and add salt if needed.
Transfer 1/2 cup (120 mL) of the finished sauce to a bowl with the shredded chicken and stir just until the chicken is lightly coated. Spread about 1/2 cup (120 mL) of the remaining sauce across the bottom of a 9-by-13-inch (23-by-33-cm) baking dish.
Heat the remaining 1 tablespoon oil in a skillet over medium heat. Briefly soften each tortilla in the oil, about 10 seconds per side, adding more oil only if the pan becomes dry. Dip each softened tortilla into the red sauce, fill with about 1/4 cup (60 mL) of the chicken mixture, roll it up, and place it seam-side down in the baking dish.
Pour the remaining red sauce evenly over the enchiladas. Bake until the sauce is bubbling and the enchiladas are hot throughout, about 15 minutes. Let stand for 5 minutes, then top with queso fresco, crema, chopped onion, cilantro, radishes if using, and lime wedges.