Rub the pork all over with the cumin, garlic, 1 1/2 teaspoons salt and 1/4 teaspoon pepper. Place in a slow cooker and drizzle with the orange and lime juices. Cook on high heat until the meat is tender and falling apart, 6 hours. Transfer to a cutting board and coarsely shred.
Spread one side of each loaf with mayonnaise and the other with mustard. Build the sandwiches with the pulled pork, ham, Swiss and pickles (you will have some pulled pork left over).
Melt 1 tablespoon of the butter in a large skillet over medium heat. Place 2 of the sandwiches in the skillet and cover with another skillet, weighing it down with a heavy can or pot. Cook until golden brown, about 4 minutes. Turn the sandwiches over, replace the top skillet and continue to cook until the other side is golden brown and the cheese is melted, about 3 minutes more. Repeat with the remaining sandwiches, adding the remaining butter to the skillet.