I guess I addressed most of what you're dealing with by adding a wrist lanyard. I can wrap it over the back of my hand and down between my index & middle fingers and it supports most of the weight for me. I just have to keep my fingers flat along the back of the Reader and I'm good. To turn pages, I just bring my thumb over to the button and click -- no having to clamp the Reader in my hand to hang onto it, so I don't have the strain that you're running into.
You might want to give that a try if you have a lanyard handy from something else (why they didn't include one just baffles me), it may help.