Preheat oven to 400° Fahrenheit. Lightly spray 9x13 casserole dish with neutral cooking spray, covering bottom and sides of pan. Tear off sheet of aluminum foil large enough to cover pan completely. Spray one side of foil with cooking spray. Set aside.
Arrange cubed pieces of 6 slices rye bread in bottom of casserole dish, covering bottom of dish completely with bread in single, even layer.
Spread 1 16-ounce can sauerkraut evenly over layer of bread, then arrange strips or pieces of 1 pound deli corned beef on top of sauerkraut layer.
Pour 1 cup Russian dressing evenly over corned beef, spreading dressing out to cover corned beef completely if needed.
Cover pan with aluminum foil, placing oiled side of foil face-down.
Place casserole dish in preheated oven. Bake casserole 20 minutes.
After 20 minutes, carefully remove casserole dish from oven. Remove foil and discard.
Sprinkle 2 cups shredded fresh Swiss evenly over top of casserole, covering dressing completely.
Return casserole dish to oven. Bake casserole 5 to 10 minutes or until Swiss cheese is melted and bubbly.
When cheese has melted, carefully remove casserole dish from oven. Let stand 2 to 3 minutes, then serve warm.