Preheat the oven to 400 degrees F. Line the inside of a 10-inch skillet, the outside of an 8-inch skillet and the bottom of 2 baking pans with nonstick foil.
Lay the bacon slices on one pan and the zucchini slices on the other. Brush the zucchini with the reserved artichoke marinade and sprinkle with 1/2 teaspoon salt and 1/2 teaspoon pepper. Roast until the bacon is crispy and the zucchini has softened, 15 to 20 minutes. Let cool slightly.
Lay out the bottom halves of the ciabatta rolls and top each with 2 bacon slices and 1 zucchini slice. Divide the artichoke hearts, roasted red peppers, cheese and arugula among the sandwiches and top with the remaining ciabatta halves.
Heat the larger skillet over medium heat and add 2 of the sandwiches. Place a hand towel inside the smaller skillet and use it to press the smaller skillet down onto the sandwiches, creating a sandwich press. Continue pressing until the sandwiches are a bit flattened and browned, 3 to 4 minutes. Remove the smaller skillet and flip the sandwiches. Press the smaller skillet down again to brown the other side, another 2 to 3 minutes. Repeat for the remaining sandwiches. Slice and serve hot.