Make the Russian Dressing: In a small bowl, mix together mayo, ketchup, onion, hot sauce, and paprika and set aside.
Butter an 9 inch pan or an 8 x 8 baking dish. Layer the ingredients for the Reuben: start with the three fourths of the corned beef, top with the sauerkraut. Sprinkle the caraway seeds across the sauerkraut. Drizzle the dressing over the sauerkraut. Top with the remaining meat, and then top with Swiss Cheese. So your layers will be: meat, sauerkraut, caraway seeds, dressing, meat, and Swiss cheese.
Bake at 400F for 15 minutes until the cheese has melted and is bubbling. Turn on the broiler and broil for 2-3 minutes if desired.
Use a combination of thinly sliced pastrami and corned beef.
Drain the sauerkraut as well as you can. Despite this, you will have some sauce in the bottom of the pan once it's baked. I drizzled most of this over the casserole.
If you don't care about making this low carb, you can always layer the bottom with pieces of rye bread. Top with rye bread as well, and bake as directed. In this case, the bread will soak up all the lovely dressing. But of course, for low carb, either skip the bread or try it with Sola bread which is currently my favorite low carb bread.
Use Swiss cheese or any other kind of melting cheese for the top.