In a large pot, combine 4 cups water with the apricot nectar, apple juice, 1/2 cup brown sugar, the granulated sugar, salt, garlic, Worcestershire sauce, pepper and bay leaf. Bring to a simmer and stir, then remove from the heat and let cool. Strain the brine and, using a marinade injector, inject it into the turkey breast and drumsticks, distributing throughout (or just place the turkey in the brine). Cover the turkey with foil and refrigerate overnight.
In a container with a tight-fitting lid, combine the bourbon, honey, vinegar and ½ cup brown sugar. Shake vigorously to blend; set aside.
Preheat the grill to low. In a bowl, combine the remaining 1/4 cup brown sugar with the paprika, mustard, chili powder, garlic powder, onion powder and saffron seasoning to form a paste. Dry the turkey with a paper towel and rub the paste all over the turkey parts. Grill the turkey, turning the breasts once, until the meat reaches 165° on a meat thermometer, about 3 hours, brushing the turkey with apple juice every half hour to keep it from drying out. During the last half hour of cooking, brush occasionally with the reserved bourbon-honey glaze.