Queen cup is different than a queen cell, a queen cup is the wax cell, and hives often have several here and there, the queen cup becomes a queen cell when an egg is laid in it. No need to worry about cups, cells on the opther hand mean intent to swarm.
In NJ I would bet you need three mediums well filled to survive the winter. I run mediums and "usually" three medium brood chambers are enough to see my bees through the winter...
Once in a blue moon its not enough, so i also winter with sugar cakes on the top frames. That way if they get there they wont starve...
2013/2014 winter worked that way.. it got COLD in mid November, and did not get above 0 (f) until Late February.. I found the bees had stovepiped, meaning they went straight up. They were unable to get to honey on the sides, ends or corners.. the sugar was what saved them... in a winter where 70% losses were the norm, I lost one hive.
Preparing for winter is one of the most important things you need to aid your bees with.