My first thought was if the sandwiches are to be served before or after the card playing. That would allow for a multitude of delicious, greasy, or dripping with sauce or other dressing sandwiches which would not be appropriate for consumption at the card table during the game.[;)]
tiki had some great idea’s, and I like your thoughts about fried clam rolls or Cubans, although I think you need a press to do a proper Cuban.
How about some nice deli style, like hot pastrami or corned beef on rye with good Kosher dill or polish pickles on the side.
Maybe Italian subs; good rolls with the eaters choice of meats, cheese, dressing, and veggies (lettuce, tomato, onion, hot and sweet peppers). It would be fun to have everything on platters and let everyone make their own.