I think your theory with how your styloids have elongated and how this could potentially have caused TOS sounds pretty feasible!
If you don’t get anywhere with a doctor in France, @Algobe has mentioned a doctor in Spain in this discussion, although we don’t know anything about him:
And also this doctor in Germany has been talked about recently:
Post Surgery with Dr. Andreas Schmitz at Bel Etage Clinic - General - Living with Eagle
Whether these are any easier for you to have surgery done instead of with Dr Aghayev, I don’t know… Sending you hugs, you’ve been through so much! 