The last summer weekend before Labor Day is a great time to enjoy relatively fewer crowds (and fewer rafts) but still have long days on the river. Upper Ocoee (Class III-IV) releases 8:30-4:30 on Saturday and 9-2 on Sunday. Middle Ocoee (III+) releases 9am - 7 pm both days.
AW River description here: https://www.americanwhitewater.org/content/River/detail/id/1780/
Camping at Adventures Unlimited, 522 US-64, Ocoee, TN 37361: https://www.adventuresunlimited.net/camping/