I had this problem for a year. I had to get a buffalo bar to take the pressure off. My shoulders killed me because of my bulk. The buffalo bar made all the difference in the world.
It is wider and has a curve:
You can get one for $220 here:
I tried everything. Nothing else worked. People will tell you to stretch, but at some point that doesn't work because of your sheer bulk and/or age.
I don't think it's flexibility or mobility at all for most guys that have this issue. My back, traps and shoulders are big, and along with the extra fat, it pushes the bar back and kills my shoulders. There is such a thing as being too musclebound or fat bound for certain exercises.
Take your grip wide, and get this bar if you can. It is the best solution. I now only squat with a straight bar at meets. All the other doo dads and top squats don't work well for heavy lifters.