Preheat the oven to 350°F (175°C) and apply a light coating of non-stick spray to a 9x13 inch ceramic baking dish.
In a large stainless steel mixing bowl, whisk together the cream of mushroom soup, cream of chicken soup, milk, and sour cream until the emulsion is smooth.
Incorporate the onion powder, garlic powder, salt, and pepper into the liquid base.
Fold the shredded chicken and cooked rice into the soup mixture until the solids are evenly distributed and thoroughly coated.
Transfer the mixture into the prepared baking dish, leveling the surface with a spatula.
Distribute the shredded cheddar cheese in an even layer across the top of the casserole.
In a small bowl, combine the cracker crumbs and melted butter; sprinkle this mixture over the cheese layer.
Bake for 30 minutes, or until the internal temperature reaches 165°F (74°C) and the topping has achieved a golden-brown hue.
Allow the casserole to rest for 5 minutes at room temperature to set the sauce before service.