The Cherokee, Seminole, Choctaw, Chickasaw, Creek could maybe be grouped together as a "Mississippian" faction. (Historically, they were called the "Five Civilized Tribes", but I wouldn't use that term now.) But it's ahistorical (like some of these tribes were enemies of each other). Again, maybe this is an opportunity for several factions who have independent AI controllers but the same Culture modifiers.
Having a Cherokee faction is interesting for many reasons, one being that it gives another dimension to the European/African/Indigenous interaction triangle in that some Cherokees owned African slaves. (Various Europeans and Euro-Americans had encouraged slaveowning as a component of the adoption of a "civilized" economy.) I wouldn't inflate this too much (e.g., giving the Cherokee the same slave-based plantation economy as the colonizers), because the vast majority of Cherokee didn't own slaves, and you don't want to enshrine one kind of Indigenous/African contact in the Southeast to be the "norm" when it wasn't. But there are ways to work this interaction into gameplay. Some escaped or freed slaves were welcome in Southeast indigenous communities (resulting in, for example, mixed-descent Afro-Choctaw towns), but some escapees were re-enslaved or resold to their white owners. That kind of random "roll" mechanic could be a way to illustrate the chancy fate of an escaped slave in the U.S. southeast.