TOS is definitely another thought and worth ruling in/out. Based on your client's posture and tightness in upper traps etc. it is a reasonable thought that the thoracic outlet could be affected.However, based on the symptoms that you have noted I wouldn't expect it to be the main problem. Definitely continue with your assessment though!
Another thing I wanted to add to my last post is that it is unlikely that trigger points are causing the poroblem but releasing them may at least give your client some relief and buy you more time while you try to sort out the real issue. (i.e. some clients will give up on you too soon if they don't get some relief right away) You mentioned upper traps and lev. scap........also check pecs (major and minor), subclavius....