If possible, do some research on California Indian bows before you begin. You'll discover that some Native American bow makers did not chase rings along the backs (especially when sinew is to be applied). Ishi is a good example.
There is also the issue of width of the limbs. The wider the limbs, the further you can draw the bow. Pat's advice is good, but a short, bendy handle bow may be too wide in the handle for your taste...if so, make sure the limbs are
very wide if you prefer a stiff/narrow handle.
As far as 38" being too short, the answer is no. There are several examples of sinew-backed NA bows that are shorter than 38".