I think that the best way to decide if your C1 is involved is to speak to more experienced VES surgeons, Dr Costantino and Dr Lui (as well as Dr Cognetti, Dr Hepworth and Dr Nakaji) will check that the IJV is flowing again before they close up, and also look for other compressions- sometimes there are more structures causing compression like other blood vessels, muscles, fascia or nerves. It doesn’t sound like Dr Manolidis does this, so if you don’t feel better after surgery, it’s a bit late then and you may need a revision surgery (which then means more scar tissue…)
It can be a bit of a difficult decision with which doctor to see for surgery , sometimes they don’t all agree! But it’s best to get several opinions and then decide who’s approach you feel most comfortable with, who you feel confident with etc. Dr Costantino has done a YouTube video, so you might find this helpful, he explains about other compressions too:
And also Dr Aghayev in Turkey has also explained his approach which might give you a bit more info too:
A Review Of IJV Compression by Dr Aghayev - General / Research Papers - Living with Eagle