I have made a replica of that bow out of hickory. My experience was that it was a fairly straight forward design. My cross section was flat. The tips were a bit thinner than the rest of the bow to get it to bend right in tillering.
I have never worked elm so I cannot say much about that, however, backing was not terribly common in the eastern US, especially in the southern US. I have made hickory bows of 50" and some that were even shorter. This shortened my draw length from 28" to 26" or 24" They worked just fine with no backing. The shorter white wood bows, in my experience) take a set but they perform well.
As for decoration. So few bows remain for some tribes in the east. Some are elaborate some are not. I have found the Native Americans were a lot like us. Some folks had fancy tools other had very plain utilitarian tools. Their bows and arrows were no different. So if I find few clear examples of bow decoration, and I am not interested in making an exact replica, then I study their other crafts and life skills for inspiration. Bead work, or clothing can often provide images that inspire decoration.
Arrows: I am aware of documented Creek use of shoot shafts. They had access to river cane (Arundinaria) and I cannot imagine they did not use that. Shoot choice could include but would not be limited to Arrowwood (viburnum) and Dogwood. Eastern quivers are not common in historic collections but woven quivers (oak splits or cane) and tanned animal hides are all within the realm of possibilities. Some folks with more specific knowledge may chime in an help you out.
Good luck with your project and be sure to post some pix as you go.