In a resealable plastic bag, combine garlic, lime and orange juices, cumin, salt, and pepper. Add pork and marinate, refrigerated, for up to 4 hours.
Preheat oven to 350 degrees. Wipe off any excess marinade from pork. Heat oil in a large ovenproof skillet over medium-high heat. Add pork and cook on all sides until lightly brown, about 5 minutes. Transfer skillet to oven and cook 12 minutes more. Transfer pork to a cutting board and let rest for 5 to 10 minutes before slicing into 1/8-inch slices.
Brush insides of each roll with 1 tablespoon butter. Layer 1 ounce of Swiss cheese on one of the cut sides of each roll. Top each with 6 ounces pork tenderloin, 2 ounces ham, 2 ounces pickle slices, and remaining ounce of cheese. Top with remaining halves of rolls. Brush top and bottom of rolls with remaining 2 tablespoons butter. Heat a panini press to medium high and grill sandwiches until heated through and the cheese is melted, about 5 minutes. Slice on the diagonal and serve immediately.