Special equipment: a large roasting pan fitted with a rack; butcher's twine
Remove the neck and giblets, then rinse the turkey with cold water and pat dry with paper towels.
In a large stock pot set over medium heat, dissolve 3 cups of salt and 1 cup of the maple syrup in 2 1/2 gallons water. Add 2 heads of the garlic. Using your hands, crush the peels from 3 of the lemons, half of the rosemary and half of the thyme, to release their natural oils. Add to the brine. Cool completely.
Place the turkey in a large brining bag, breast-side up. Add the cooled brine and seal tightly. Refrigerate for 12 hours. Remove the turkey from the brine, pat dry and place on a sanitary work surface.
Preheat the oven to 325 degrees F.
In a medium bowl, mix the butter and the sage. Carefully rub some of the sage butter under the skin of the turkey, being careful to avoid tearing it. Rub the remaining butter all over the exterior of the turkey. Sprinkle the whole turkey, including the cavity with salt and pepper. Tuck the wings behind the back.
Pour the stock and orange juice in the bottom of the roasting pan. The liquid will create a base for the gravy and prevent any burning on the bottom of the pan as the turkey cooks. Add the remaining quartered lemon, the remaining 4 cloves garlic, the bay leaf, onions, the remaining rosemary and the remaining thyme into the cavity.
Place the turkey breast-side up onto a rack set into a large roasting pan.
Lay down a large piece (about 12-square inches) of parchment paper. Line up 8 strips of the bacon horizontally, so that they are touching. Starting from the left side, fold 2 inches of every other strip of bacon to the right. Then lay down 1 strip of bacon vertically over the flat strips to create a left margin. Unfold the folded ends of bacon. Starting from the top horizontal strip, fold over every other strip of bacon that hadn't been folded down already to the left and lay down a vertical strip. Fold the strips back over. You should have two rows of woven bacon. Repeat this process until you achieve a tight square of woven bacon.
Invert the bacon lattice onto the breast of the turkey, tucking the ends of bacon into the crevices of the legs and thighs, like making a bed. Truss the legs with butcher's twine. Cover the turkey with foil and bake for 2 hours 15 minutes.
Remove the foil and continue cooking the turkey for another 1 hour 15 minutes, basting the bacon with the remaining 3/4 cup maple syrup every 10 minutes until the bacon is crispy and the internal temperature of the turkey is 165 degrees F.
Loosely tent the turkey with foil and rest it for 30 minutes before carving.