In a large bowl, combine the lime juice, sesame oil, soy sauce, ginger, orange juice, vinegar, olive oil, sugar, and orange zest. Arrange the pork in a 9x13-inch dish and pour 1/2 cup of the marinade over the meat. Add the pineapple rings and scallions to the remaining marinade and toss. Marinate everthing in the refrigerator for 30 to 45 minutes, turning the ingredients occasionally.
Meanwhile, prepare a medium charcoal or gas grill fire. Brush the grill grate clean.
Remove the pork, pineapple, and scallions from their marinades. Season the pork lightly on both sides with salt and pepper. Grill, covered, until the pork is just barely cooked through, 3 to 4 minutes per side, and the pineapple and scallions are warmed through and grill-marked, 2 to 3 minutes per side for the pineapple and 1 to 2 minutes per side for the scallions. As each item finishes cooking, transfer it to a serving platter. If your grill isn't big enough to fit everything at once, grill the scallions last.
Serve with Steamed Jasmine Rice and Minty Melon Sorbet.