@Dontgiveup First of all, I really feel your pain and anxiety. Sometimes worry + ES clouds our thinking and we can’t really quantify risks very well. So let me say this, nothing is permanent (health, pain, suffering…etc. it is the nature of the universe). So this will resolve in time and would unfortunately take sometime before you see symptoms disappear even with surgery so patience is key (I know it is hard when suffering).
Now the good thing is you are under the care of one of the most experienced ES surgeon and reputable Vascular doctor Dr Higgins so I trust their judgement of your case. If during the operation, they see that the Jugular Vein blood flow appears to be normal, then they will abort C1 shaving is my assumption as I understand it from your posting. So I trust Dr Axon since he has done countless operations of this kind. If they feel they need to shave down the C1, I would not worry about cascading effect and misalignment as that might be minor compared to what can happen if blood flow is left impaired for long time (Dr Axon is well aware of this). So the cost benefit analysis is warranted here.
Secondly, there are no good studies out there but I found one study (My long journey to diagnoses of Jugular Vein Compression by Styloid & C1 - #6 by KoolDude) where 10 or 11 people went through Styloid removal as well as C1 shaving and the outcome was promising as most had positive outcome and no complication relating to C1 was reported. Also, we have few folks that went through it recently such as @M_UK who does not appear to be affected by any complication relating to the C1 in particular. So all this should give you a confidence to go ahead and if anything, the recovery might be bit longer than Styloid removal alone but that is better price to pay than not having all your symptoms improve and face revision surgery in the future.
As far as the Catheter Angiogram is concerned, I would rather have the decision made by the doctors but my untrained opinion is, that since the compression is visible in your CTV, they only needed to see blood flow and pressure gradient with catheter angiogram since they can’t tell if that is only the problem you might be having. The other thing is, that rules out a whole host of vascular diseases that is not even related to ES. So it is good to have it from that point of view. But on the other side, we have lots of people that never had catheter angiogram and had the surgery without any issues. So this one is really personal thing. I am a health nut so I would like to rule out other stuff so that is why I wanted to do the catheter angiogram but in your case, it might not be necessary since the compression is visible.
All in all, I want you to know things will be ok. Trust the doctors and as the old adage goes Be patient with yourself. Nothing in nature blooms all year