Make the Russian Dressing: In a small bowl, combine mayonnaise, ketchup, sweet pickle relish, Worcestershire sauce, and smoked paprika. Stir well until thoroughly combined. Set aside.
Assemble the Casserole: Preheat oven to 350°F (175°C). In a greased 9×13 inch baking dish, layer half of the cubed rye bread. Top with corned beef, then sauerkraut. Drizzle with half of the Thousand Island dressing and half of the Russian dressing. Sprinkle with half of the shredded Swiss cheese. Repeat layers, ending with a layer of Swiss cheese.
Bake: Cover the baking dish with aluminum foil and bake for 30 minutes. Remove foil and bake for an additional 10-15 minutes, or until cheese is melted and bubbly.
Serve: Let the casserole cool slightly before cutting into squares. Enjoy!
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