Preheat oven to 350°F and generously spray a 13x9 (3-quart) baking dish with cooking spray. Prepare rice according to package instructions and set aside.
In a nonstick skillet, melt butter over medium-high heat. Sauté onion, mushrooms, thyme, salt, and pepper until tender. Stir in flour until well combined. Gradually add milk, stirring constantly until simmering. Mix in chicken broth, Worcestershire sauce, sour cream, cream cheese spread, and poppy seed. Simmer until slightly thickened, stirring frequently.
Combine chicken, cooked rice, and sauce in a large bowl, then spoon the mixture into a baking dish. Bake for 25-30 minutes at 165°F. While baking, toss crackers with 2 tablespoons of melted butter in a resealable bag, then sprinkle over the casserole during the last 5 minutes of cooking.
To prepare ahead for later: Line a 13x9-inch (3-quart) baking dish with 2 layers of plastic wrap, allowing some to hang over. Spread rice mixture in a large shallow pan and cool completely in the refrigerator for 30 to 45 minutes, covered. Transfer cooled mixture into the lined dish and cover with another layer of plastic wrap. Freeze the unbaked casserole for about 8 hours until solid. Place the frozen casserole in a labeled 2-gallon resealable plastic bag, removing air before sealing, and freeze for up to three months. When ready to bake: Grease a 13x9-inch (3-quart) baking dish with cooking spray. Thaw the casserole in the refrigerator for 24 to 48 hours. Preheat the oven to 350°F. Remove the plastic wrap, cover the dish tightly with foil, and bake for 50 minutes. Sprinkle the cracker mixture on top and bake for an additional 5 to 10 minutes until golden brown and the casserole is heated through (165°F in center).