I think you all are overlooking a key feature of the Cherokee that would make them a great contender for Brave New World. The Cherokee is known as one of the five civilized tribes. They got this title because, along with four other tribes, they quickly adopted American culture and technologies. And they played a part in the Civil War in the Oklahoma-Kansas-Arkansas area.
They could have the ability that lets them adopt other cultures more quickly and integrate it into their own and get a boost to science for each more advanced civilization they meet. (Or something like that)