The turkey will be cooking directly on the rack of your grill. Place a roasting pan that will be under the bird (this will also catch the drippings). A disposable aluminum roasting pan or even an aluminum baking sheet with a lip edge will work. Alternatively, you can cook the turkey on a roasting pan with a rack if your grill area is large enough. Preheat grill to 450º F (or as high as it will go if it doesn't go to 450).
Remove turkey from bag, and discard brine, orange quarters, and bag. Rinse turkey with cold water and pat dry. Cut a small slit in the breast skin so that you can tuck wing tips under to keep in place. Tie legs together with kitchen string if the turkey didn't already come with a fastener.
Place herbs in the cavity of the bird. Slice butter and slide in between skin and meat on turkey breast.
Mix together dry rub ingredients and rub over entire turkey, patting down to get it to stick.
Arrange turkey, breast side down, directly on grill. Roast at 450º for 30 minutes.
Reduce BBQ temperature to 350º F.
Carefully turn turkey over (breast side up). Roast at 350º for 1 hour and 15 minutes* (see note) or until a thermometer inserted into meaty part of breast registers 150º. Remove turkey from grill, tent with foil with thermometer still inserted, and let stand until internal temperature reads 160-165º , about 20 minutes. Reserve pan drippings for gravy.