IT would be good to find another comparable sign apart to the Ext.
More questions are required, what about PAms with extension you coulf pick up the level >
ADD some Mulligan SNAG when you find the level, it may work.\
if you think the level is c6 you could do combined movements start the treatment in flexion and work up to extension -PPIVMS
Neural tension tests +ve?

Another not very common condition, thoracic outlet syndrome.

I
Did you try anterior mobilisation of C/S