Remove insides of bread halves; reserve for another use. Stir together mayonnaise, lemon zest and juice, and capers in a bowl; season with salt and pepper. Divide mixture evenly between top and bottom bread halves. Layer half of turkey, cheese, and capocollo on bottom, then repeat layering with remaining meats and cheese. Pack watercress into top half; layer with tomato slices and season with salt and pepper.
Close sandwich. Wrap tightly in plastic wrap, then foil. Place a heavy skillet on top; press down to flatten sandwich slightly. Add several heavy canned goods to top of skillet. Let sit at least 45 minutes or, in refrigerator, up to 12 hours before unwrapping, slicing into wedges, and serving with chips and fruit.
OR.... Make it into a Grilled Italian Sandwich. Butter one side of each slice of bread. Spread mayonnaise on the other before layering the sandwich as noted above. Grill in a stovetop skillet over medium to medium-low heat until golden brown on each. If you don't have a sandwich press grill, you can still get a pressed sandwich by using a cast iron pan to press for 2-3 minutes while the cheese melts. We also recommend adding smashed avocado for extra flavor.