Look on Primitive Archer, there are guys in the US there making and shooting them.
I make some primitives which are a bit like some of the native American bows, but there were many types anyway. on the East coast there were bows similar to our longbows, most of their bows were much shorter and many were sinew backed. There is plenty of published info out there.
IMHO The American Flat Bow (they call it a long bow) and the modern bows have very little to do with native American bows and are more closely related to the Victorian longbows which went over to the States. Hickman designed the first modern
recurve an scientific principals not from elwhere (Clarence N Hickman the father of scientic archery ISBN 0-9613582-0-3) he was striving for speed from a low draw weight to help compensate for ill health and injury. He also designed high speed cameras and was the first to film an arrow flexing to get round the bow (archers paradox). His cameras were used for filming experiments in rocketry, during one such experiment he lost some fingers.
Del