Preheat oven to 350°F (175°C).
In a very large bowl, whisk together the marinade ingredients: 1/3 cup honey, 1/2 cup lime juice, 2 teaspoons chili powder, 1 teaspoon onion powder, 1 teaspoon garlic powder, 1/2 teaspoon salt, 1/2 teaspoon smoked paprika, 1/2 teaspoon cumin, 1/2 teaspoon chipotle powder, and 1/4 teaspoon cayenne pepper (optional).
Add the 1 pound cooked, chopped chicken breasts to the marinade and toss to coat. Let the chicken sit in the marinade for 10 minutes.
While the chicken marinates, combine the cheeses in a separate bowl: 1 1/2 cups shredded Monterrey Jack and 1 1/2 cups shredded sharp cheddar. Set aside 1 cup of the mixed cheese for topping and use the remaining 2 cups in the casserole.
To the bowl with the marinated chicken, add 3 1/2 cups cooked long grain or brown rice, 2 cups salsa verde, 1/2 cup sour cream, the drained 14 oz. can of mild diced green chilies, and the rinsed and drained can of sweet corn. Add the 2 cups of mixed cheese. Stir until everything is evenly combined (the mixture will be a bit wet).
Spread the chicken-and-rice mixture into a 9 x 13-inch casserole dish and sprinkle the reserved 1 cup of mixed cheese evenly over the top.
Bake for 30 minutes, or until the casserole is hot in the center. If desired, broil for 1–4 minutes more to brown the cheese—watch closely to prevent burning.
Remove from oven and let rest 5 minutes. Serve with tortilla chips, extra sour cream, chopped cilantro, and sliced avocados as desired.