I have not been keeping up on NJ weather, but if it's warm enough to try, could you swap the boxes? Bees like to store over the brood chamber and may take syrup to fill some of that space. If they don't fill, or don't fill enough to warrant keeping the box on (like greenbtree suggests, too much space to keep warm in), you can always store the one or two frames they did fill to feed back later. And, it will be easier to pull at that point because it will be on top.