About 14 hours before grilling, in a very large nonreactive bowl whisk all of the brine ingredients, except for the ice water, until the salt and sugar are dissolved. Stir in the ice water. The brine should be very cold.
Remove the giblets, neck, and lumps of fat from the turkey and reserve (discard the liver). Place in a bowl, cover, and refrigerate until ready to grill. If your turkey has a metal or plastic trussing clamp, leave it in place. Place the turkey inside a sturdy plastic bag and set it inside a large stockpot. Pour enough of the cold brine into the bag to cover the turkey as much as possible when the bag is closed and tightly tied. Discard any extra brine. Seal the bag. (If you don’t have room in the refrigerator, or if you don’t have the right sized pot, put the turkey in the bag in an ice chest and surround it with ice.) Refrigerate the turkey for at least 12 hours and no longer than 14 hours.
Remove the turkey from the bag and discard the brine. Rinse the turkey under cold water and pat it dry inside and outside with paper towels. Put one-third of the chopped onion into the neck cavity, and pin the neck skin to the back skin with a skewer. Put the remaining onion into the body cavity. Tuck the wing tips behind the turkey’s back and tie the drumsticks loosely together with butcher’s twine (or insert them in the plastic or metal truss, if there is one). Brush the turkey all over with the melted butter. Place one large disposable foil pan inside of the other creating a double thickness. Place a roasting rack in the pan. Place the turkey, breast side down, on the rack. Allow the turkey to stand at room temperature for 1 hour before grilling.
Soak the wood chips in water for at least 30 minutes. Prepare the grill for indirect cooking over medium-low heat (about 350°F).
Place the reserved giblets, neck, and lumps of fat in the roasting pan and pour in the chicken broth. Drain and add two handfuls of the wood chips to the charcoal or to the smoker box of a gas grill, following manufacturer’s instructions, and close the lid. When the wood begins to smoke, cook the turkey over indirect medium-low heat, with the lid closed, for 1 hour, keeping the grill’s temperature as close to 350°F as possible.
After 1 hour, turn the turkey over so that the breast side faces up. Drain and add two handfuls of wood chips to the charcoal or smoker box. Cook the turkey for another 45 minutes and then drain and add the remaining two handfuls of wood chips to the charcoal or smoker box. Continue cooking the turkey, with the lid closed, until an instant-read thermometer inserted into the thickest part of the thigh (not touching the bone), reaches 170°F, 1 to 1¾ hours longer. If the juices in the pan evaporate, add 1 cup water to the pan. During the last 15 minutes of cooking time, lightly brush the turkey with the maple syrup, trying not to let any syrup drip into the pan.
Remove the pan with the turkey from the grill. Tilt the turkey so the juices run out of the body cavity and into the pan. Transfer the turkey to a cutting board and let rest for 20 to 30 minutes (the internal temperature will rise 5 to 10 degrees during this time). Save the pan juices to make the gravy.
In a large skillet over medium heat, cook the bacon until crisp and browned, about 10 minutes, turning occasionally. Transfer to paper towels to drain and cool. Reserve the bacon fat to use for the gravy, if needed. Chop the bacon.
Strain the pan juices into a gravy separator. Let stand until the fat rises to the surface, about 3 minutes. Pour the pan juices into a 1-quart measuring cup, reserving the fat. If necessary, add chicken broth to the 1-quart measuring cup so that you have 1 quart of liquid.
Measure the reserved fat. If necessary, add enough of the reserved bacon drippings to make ½ cup. In a medium skillet or saucepan over medium-high heat, heat the fat. When the fat is hot, whisk in the flour and let it bubble for 1 minute, whisking constantly. Increase the heat to high, whisk in the pan juices, and bring the gravy to a strong simmer, whisking often. When the gravy reaches a strong simmer, reduce the heat to medium-low, add the chopped bacon, and simmer until slightly thickened, 3 to 5 minutes more. Remove from the heat and season carefully with salt and pepper, if needed (the brine and bacon may have seasoned the gravy enough).
Carve the turkey and serve with the warm gravy.