Make the coleslaw. In a large bowl, whisk together the sour cream, mayonnaise, apple cider vinegar, sugar, celery seeds, kosher salt, and black pepper.
Fold in the shredded cabbage and carrots until evenly coated. Let the coleslaw stand for at least 30 minutes, then drain off any excess liquid before assembling the sandwiches.
Make the Russian dressing. In a separate bowl, whisk together the mayonnaise, sweet pickle relish, prepared horseradish, sambal oelek, ketchup, Worcestershire sauce, kosher salt, and black pepper until smooth.
Prepare the bread. Remove the crusts from the loaf of rye bread and trim it into a rectangular block. Slice the bread horizontally into very thin, 1/4-inch slices.
Assemble the sandwich. Lay one long slice of bread on a flat surface. Add one-third of the corned beef or roast beef in an even layer.
Spoon some coleslaw over the meat and spread it evenly. Add a layer of Russian dressing, then top with a few slices of Swiss cheese.
Place another slice of bread on top. Repeat the layering process with the turkey or ham, followed by more coleslaw, Russian dressing, and Swiss cheese.
Continue layering until the sandwich is assembled. Slice into portions and serve.