Stir the melted butter into the cornbread stuffing and set aside. In a small bowl, mix the cream of mushroom soup with 1 1/4 cups of the reserved broth and set aside. In another small bowl, dilute the cream of chicken soup with the remaining broth and set aside. In a large, oblong baking dish, put a layer of the stuffing; a layer of chicken and the cream of mushroom soup mixture. Top with more chicken, the cream of chicken soup mixture and remaining stuffing. Bake in 350 degree oven for 45 to 60 minutes until bubbly and browned.
NOTE: 4 or 5 large boneless, skinless chicken breasts can be used in place of the whole chicken. Just cook them completely and then chop or shred them to put in the casserole. Or if you're REALLY pressed for time, a grocery store rotissiere chicken works well, too!