Whisk orange juice, lime juice, garlic, cumin, oregano and salt in a shallow container. Add pork, turn to coat and refrigerate for 30 minutes.
Heat a grill or grill pan to medium-high. Lift pork from the marinade, discard the marinade, pat the cutlets dry and brush with oil.
Grill pork for 3 to 5 minutes per side until the centers reach 145°F, then rest for at least 3 minutes. Warm ham briefly on the grill for about 30 seconds per side.
Slice pork thinly across the grain. Split the rolls and spread mustard over the cut faces, then layer half the Swiss, sliced pork, ham, two pickle slices per roll and the remaining cheese.
Close the subs and spread butter thinly over their outsides. Heat a large skillet over medium-low and cook two sandwiches at a time under a second heavy pan.
Press for 3 to 5 minutes per side until lightly crisp, the cheese melts and the centers reach 165°F, lowering the heat if the bread colors too quickly. Repeat with the remaining two sandwiches.
Rest for 2 minutes, then cut diagonally across the middle and serve one sub per person.