BTB, lots of good suggestions so far, but...
do you do a shoulder/arm warm-up before you squat? some mobility work would improve your flexibility.
Also, I'll call friendly BS on your claim that you can't low bar squat due to your back...when I am pinching my shoulder blades properly, the bar gets wedged into place with almost no strain on my arms or wrists...
Low Bar Placement
Typically used for powerlifting squats. The goal is to maximize your leverages, so the closer you can get the load to your own center of gravity (COG) and minimize the moment arm (distance from the bar to your hips (ie. the fulcrum), the more weight you can lift.
High Bar Placement
Because of the up/down bar path and upright torso positioning of a typical high bar back squat a high bar position is preferred. This not only allows the lifter to move their hands in and elbows down, tightening up the upper back (and creating more tension) but also keeps the torso more upright. If the bar was lower, the lifter would have a great tendency to fall forward in the hole.
I probably look something like this...