Lots of good stuff to learn here on the forum, they got me started on TOS forum 11 years ago. Most folks know more about their situation then the majority of docs!

OMG on your hands, he is starting at the bottom of the chain working up?

Well, if if he is focusing on your hands and ruling out the artho, I hopes he works his way up to the cervical and brachial area soon!
To tell you the truth if I have TOS and doc looks at my hands first, I am leary to how much he really cares about TOS as a diagx. The reason I say that is if you explain your symptoms and he is starting at the hands, he may be anti TOS.

We have a super top Neurologist in the area. A forum member saw him. She was diagx with MS and TOS. Straight up he told her I will treat the MS but not address the TOS. Unreal! For all his education to help, he just refuses and slams a door.

We are lucking to have several top knowledgable docs in the area here and Norristown/Blue Bell Phila area. They cut to the chase when they suspect TOS.
But, I forget your sympt. Maybe there is a new concern of a symptom.
What I hated was several years of trying to get a diagx for my daughter when the first doc a ortho in our area treating her KNEW what it was and did not say or treat. NOR protect her from further injury!