"Doesn't believe in pec minor blocks..."

Are you sure your pain management doctor understands that it would be for diagnostic purposes and not for pain management? Because pec minor blocks only last for a couple hours which could be why your doctor is thinking "wtf is this woman talking about... a pec minor block isn't going to help her!" I would suggest talking to a vascular surgeon or another specialist who diagnoses TOS about the pec minor block. Have you tried just calling a bunch of neurologists/vascular surgeons in the area and talking with their nurse about whether they diagnose TOS and how many patients with TOS they see?