Don't know how much money they are but you could invest in a Manta Ray for back squats. The bar will go no where, but stay put throughout a set. If you have higher thick traps there may be a problem though. Also another device for front squat, made by the same company, is supposed to work well. Seen the Manta Ray but not the front squat version.
PL'ers really should not have to worry about shoulder tightness. Olympic lifters are some of the most flexable lifters around and they spend a lot of time on warm-up stretches and other moves with a bar every workout. May want to do a search to check out they stretching moves. Presses behind the neck seem to help some benches overcome this problem and also add to their lift. As do door jam stretchers (sideways and overhead). Even hanging from a chinning bar, from extra wide to a interlocking finger grip can help.
I find the thicker the upper back and the heavier the weight, the less worry about bar rolling downwards. But than again, everyone's built different. Good luck.