What about the drink? Do not reach for milk. That is a chunky disaster waiting to happen.
Go for a dark beer. A stout or a porter. The roasty flavor is a perfect mirror for the rye bread. It’s like the sandwich is drinking its own reflection.
Or a celery soda. Yes, it exists. It’s weird, fizzy, and oddly savory. It tastes like a vegetable having a party in a glass.
Dessert? You have to be joking. But if you insist, get a black and white cookie. It’s the only thing light enough after a Reuben. The soft cookie is a gentle finish to a very intense meal.