Combine salt, garlic powder, onion powder, cumin, oregano, crushed red pepper, peppercorns, bay leaf, and lime/orange zest and juices in a bowl.
Place sliced onions and garlic cloves in the bottom of slow cooker. Top with pork shoulder and pour juice and spice mixture over the meat. Set slow cooker on low for 6 to 8 hours. When done, remove pork from cooker and let cool slightly. Then shred cooked pork into thick chunks using 2 forks. Pour remaining juices over pork to keep warm.
Preheat a panini press according to manufacturer's instructions.
Spread Dijon mustard on both sides of each hamburger bun. Then layer from bottom to top with pickles, red onions, 1/2 cup pulled pork per sandwich, sliced ham and Swiss cheese.
Brush outsides of buns with olive oil and place in panini press until cheese is melted.