In a small bowl, whisk together the rum, soy sauce, pineapple juice, lemon juice, mustard, molasses, ginger, garlic, and pepper. Reserve 1/4 cup of the marinade for basting.
Place the remaining marinade and pork chops into a resealable bag, and transfer to the refrigerator. Marinate for 6 to 8 hours, flipping periodically.
Preheat the grill to medium-high heat.
Make the grilled pineapple:
Dab the pineapple rounds with a paper towel to remove excess moisture. Brush the rounds with avocado oil or olive oil and season lightly with salt and pepper on both sides.
Grill the pineapple slices for 6 to 8 minutes, flipping once, or until they are golden brown on both sides. Transfer to a platter. Use about 3 slices for the grilled pineapple salsa, and set aside the remaining slices for serving.
Make the grilled pineapple salsa:
Combine 3/4 cup of finely chopped grilled pineapple, onion, jalapeño, cilantro, honey, salt, and a pinch of pepper in a small bowl. Let it rest for about 20 minutes, as you grill the pork chops.
Grill the pork chops:
Adjust the grill temperature so that you have one area of high heat, and another for medium heat.
Brush the pork chops with olive oil on both sides. Place the chops on the grill over high heat, cover, and sear for 3 minutes on each side. Transfer the pork chops to the medium heat (or lower heat to medium), cover the grill, and cook for an additional 4 to 7 minutes, flipping periodically, until the pork chops are fully cooked with an internal temperature of 145°F. Remove the pork chops off the grill and let it rest for 5 minutes before serving.
Serve the pork chops with the grilled pineapple slices and the pineapple salsa.
Take care not to over-marinate the pork — because of the acid in the marinade, leaving the pork too long in the mixture could break down the meat, altering the texture, making it too mushy. For best results, do not marinate more than 12 hours.The grilled pineapple and grilled pineapple salsa can be made up to a day in advance and stored in the refrigerator until ready to serve.