I backed a bow with the epidermis left on. I am making some buckskin today, and where I got the epidermis off real good, it is soft and flexible. On the spots that I didn't get it off, the leather is stiff and strong. I brained it yesterday and left it in to soak overnight and softened the hide today. I can really see that for making buckskin, getting the epidermis off is very important. Probably for two reasons, first, to get rid of the stiffness and second, to let the brains penetrate better. My elk hide is next and I am going to work to get the epidermis off real good on that hide.
In my opinion, I think I would leave the epidermis on for backing a bow.