In a bowl, mix salt, 1 cup brown sugar, 3 tablespoons garlic powder, 3 tablespoons onion powder, 1 tablespoon savory, 2 teaspoons dried tarragon, and all of the dill weed.
Rinse salmon and pat dry. Set salmon, skin down, in an 11- by 17-inch roasting pan lined with plastic wrap. Spread salt mixture evenly over flesh of salmon. Cover and chill 3 hours.
Rinse fish under cool water and pat dry. Set fillet, skin down, on a large sheet of foil; cut foil to fit outline of fish. Let fish stand until flesh is tacky to touch, 20 to 30 minutes.
Meanwhile, in a small bowl, mix remaining 2 tablespoons brown sugar, remaining 1 1/2 teaspoons each garlic powder and onion powder and remaining 1/2 teaspoon each savory and tarragon.
If using charcoal, mound 50 briquets on the firegrate of a barbecue with a lid and ignite; if using a gas grill, turn heat to high and close lid. Pour enough warm water over wood chips in a bowl to make them float; let soak at least 15 minutes.
When coals are dotted with gray ash, in about 20 minutes, push half to each side of firegrate. Drain wood chips and scatter half on each mound of coals. If using a gas grill, adjust for indirect heat; put drained chips in a foil pan and set directly on heat.
Cover barbecue and heat until chips start to smolder, about 10 minutes. Set grill 4 to 6 inches above the firegrate.
Place salmon on foil in center of grill (not directly over heat). Sprinkle sugar mixture evenly over fish.
Cover barbecue and cook salmon until a thermometer inserted in center of thickest part reaches 140°, 20 to 25 minutes.
Using two wide spatulas, slide fillet with foil onto a rimless baking sheet, then transfer from sheet to a platter. Tuck edges of foil under fillet. Serve hot or cool.