If you think C1 rotation could be causing an issue then it might be worth contacting Iain Smith at Newport Chiropractic. He is an atlas orthogonal chiropractor - they don’t do any rough manipulations, instead they use a precision tool that gently impacts the atlas.
My understanding (though it is likely flawed) is that where C1 rotation is the issue, atlas orthogonal (AO) treatment can be useful. If however the issue is jugular compression caused by a narrow gap between styloid and C1 then AO probably won’t help.
A word of caution: chiropractic interventions have been known to cause instant problems, sometimes very serious ones. I think this is more for the fast neck-cracking type, which Iain Smith does not do, I believe.
I had a telephone consultation with him, but decided not to pursue it as my C1 wasn’t particularly rotated. He does generally get good reviews, but as usual there are no guarantees that he will help, and it is expensive, I think somewhere in the region of £2-3,000 for a full workup and set of AO sessions.
Searching in this group will throw up some patient experiences: