Combine the chicken, chicken stock, wine, cilantro, lime juice, garlic, peppercorns, 1 teaspoon of the salt, the oregano, and bay leaves in a medium saucepan and bring to a boil. Reduce the heat to a simmer and cook, uncovered, for 10 minutes. Remove from the heat and allow the chicken to cool in the poaching liquid for 45 minutes. Remove the chicken from the cooking liquid and tear or cut into bite-size pieces. Reserve the chicken. Strain the cooking liquid and reserve.
Preheat the oven to 350 degrees F.
Heat the butter in a large skillet over high heat until foamy. Add the mushrooms, the remaining 1/4 teaspoon salt, and the black pepper and cook, stirring occasionally, until the mushrooms release their liquid. Continue to cook until the mushrooms are golden brown and all the liquid has evaporated, about 6 minutes. Sprinkle the mushrooms with the flour, stir to blend, and cook for 1 minute. Add the milk and stir, scraping up any bits from the bottom of the pan. Cook until the mixture begins to thicken. Add 1 1/2 cups of the reserved chicken cooking liquid, stir, and cook until very thick and flavorful, about 10 minutes. Remove from the heat.
Place the tortilla chips in the bottom of a 9 by 13-inch glass casserole. Crush the chips with your hands so they form a thin layer on the bottom of the dish. Pour 1 cup of the reserved cooking liquid over the tortilla chips and allow them to soak up the liquid. Scatter the chicken over the top of the tortilla layer. Spread the chopped onions, bell peppers, and jalapenos evenly over the chicken. Top with half of the grated cheeses. Sprinkle with the Southwest Seasoning, chili powder and ground cumin. Spoon the reserved mushroom mixture evenly over the top of the spices, then top with the tomatoes and green chiles. Cover with the remainder of the cheeses. Bake uncovered for 40 to 45 minutes, or until the cheese is bubbly and the casserole is heated through. Let sit for 5 minutes before serving.
Tip: This casserole may be prepared in advance and frozen until ready to use. Simply allow it to thaw 1 day in the refrigerator and come to room temperature before baking.