I'd expect significant lines for much of the day on those dates at Pepe's, Sally's, Modern and probably even BAR. All are popular over the holidays, so I'd try to hit Pepe's and Sally's in the mid-afternoon, in between lunch and dinner, as they are the most popular--and the least good at moving the lines. I would make Modern and BAR the bookends of those four, in whichever order. You have to get the white clam pie at Pepe's and the mashed potato and bacon pie (red is my preference) at BAR. If you are looking for anything other than pizza, the BAR salad is also excellent. Modern does everything pretty well imo, but if you like your pies crispy remember to order them "well done, light mozz." For some reason, I always seem to like the Sally's pies with bacon the best.
If you are looking to add two more, I'd probably add Zuppardi's in West Haven (sausage pie, white clam pie) and then choose one other among Olde World (North Haven), Grand Apizza (Fair Haven), Tolli's (East Haven), Zeneli (New Haven), Da Legna (New Haven), Next Door (New Haven), Kitchen Zinc (New Haven), One 6 Three (New Haven), Ernie's (New Haven) or Roseland (Derby). If you go to Roseland you have to get the seafood pie with lobster, shrimp and scallop. It's ridiculously expensive and it's nothing like pizza, but it's amazing and definitely a signature item for them.