Rub the pork with the salt, pepper, cumin and oregano and arrange it in a 6-quart slow cooker.
Add the garlic, onion, orange juice, lime juice and bay leaves.
Cover and cook on low until the pork pulls apart with almost no pressure, 7 1/2 to 8 hours.
Transfer the pork to a sheet pan, discard the bay leaves and shred the meat into large pieces.
Spoon 1/3 cup skimmed cooking fat and juices over the pork and spread it in one layer.
Broil until the tips turn dark and crisp, 4 to 7 minutes, turning the pan once.
Warm the tortillas in a dry skillet and fill each with crisp-edged carnitas.