Preheat oven to 375°. In a large frying pan over medium-high heat, cook onion with olive oil, stirring often until softened, about 5 minutes.
Stir in 3/4 cup red chile sauce, the pine nuts, raisins, cinnamon, allspice, chipotle chiles, adobo sauce, tomato paste, brown sugar, and vinegar. Add chicken, then bring mixture to a boil, stirring. Remove from heat. Pour remaining red chile sauce into a pie pan.
To make enchilada stacks, dip 1 tortilla in chile sauce in pie pan to coat. Place on an ovenproof dinner plate. Repeat with another tortilla on a second plate. Spread each tortilla evenly with a heaping 1/3 cup chicken mixture, then with 1/4 cup cheese. Repeat layering with 8 more tortillas, dipping them in sauce, then adding chicken mixture and cheese to make 2 stacks of 5 layers. (You'll use all the chicken but not all the cheese.) Dip the last 2 tortillas in sauce, place each, curved side down, on stack, and sprinkle with remaining cheese.
Bake enchiladas until hot in the center and cheese bubbles on top, 10 to 15 minutes.
Meanwhile, pour remaining chile sauce from the pie pan into a microwave-safe pitcher and cook in a microwave oven on full power until simmering, 1 to 2 minutes. To make the salad, stir together radishes, lime juice, and extra-virgin olive oil in a large bowl. Just before serving, stir in cabbage and cilantro. Season to taste with salt and pepper.
Top each enchilada with a small mound of salad and cut in thirds or quarters to serve. Offer with remaining salad and chile sauce to add to taste.
Note: Nutritional analysis is per 1/4-stack serving.