In a large bowl, whisk together all the ingredients for the marinade.
Put the pork into a casserole dish. Fill a syringe with the marinade and inject 3/4 of the way into the pork. Inject the meat in several places with the marinade. Pour the remaining marinade over the meat. Cover with plastic wrap and refrigerate for 2 to 12 hours, so flavors can permeate.
Preheat a grill to 275 degrees F, using indirect heat and applewood soaked chips.
Drain off excess liquid from the meat and pat dry with a towel. Season the pork with Neely's Dry Rub seasoning, to taste, making sure you cover the sides. Arrange on the grill with the fat side facing up. Grill until the meat is tender, about 6 hours. Transfer to a serving platter and serve.