> Some benzos have muscle relaxant properties but I've never heard of them prescribed for pain.

Back pain is thought to be mostly psychological, so it makes sense. Also, if you have minor tears or congenital defects in tissue around your spinal cord then anxiety can cause inflammation, which can then cause your spinal fluid to push against your actual spinal cord and cause all sorts of problems. (Or something like this, I'm not a doctor but that's the basic idea.)