If you are even halfway interested in reproducing authentic Native American archery equipment, I can't overstate how important the book "Encyclopedia of Native American Bows, Arrows, and Quivers" by Steve Allely and Jim Hamm. There are several volumes, Vol 1 covers the south eastern tribes, like you are describing. There are no photographs, but the line drawings are VERY well detailed, the descriptions and dimensions are clear and concise.
Plus, for history geeks like me, they list the source of every piece. Most are in museums, but a few are from private collections. I have contacted two of the museums listed for additional details on bows in their collections and was given nothing but the best cooperation possible. Heck, I even had an invitation from one museum to come see parts of the collection that not usually on display!
But most importantly...POST PICS of your bow! Now get to work!