I am no expert on the Smokies, but I think you have misstated your amounts. 100 liters of water would be about 26 gallons. I doubt you'll need that much.

Were you thinking of 100 fluid ounces (approx. 3 gallons)? If this amount is meant for consumption on the trail only, not in camp, where I'd expect a water source to be available, then it sounds like much more than one person in June would need for walking under forest cover, but at least it is much closer to your needs than 26 gallons. 100 fl.oz. is more akin to what you'd take for a day in the desert.