This is a common nuissance with refilling the hydration bladders in the sleeve inside the full backpack.
On this forum, or her personal blog, I read a post from "Christine (German Tourist)" a while back. Her work-around was simple and genius.
Take the hydration bladder OUT of the pack, and either strap it outside the pack, or the external kangaroo pouch or mesh pouch. So it is not getting squeezed by the other gear.