Really hard to judge how many symptoms are being contributed by ES vs CCI. One thing to consider, which I talk a lot about on this forum, is that ES has the potential to cause years and years of muscles compensations and imbalances. For example, when the styloids are too close to C1, they compress the IJVs (which I suspect is what you are experiencing - I haven’t gotten to see your CT imaging). To compensate for this compression, the only way to increase the stlyoid-C1 space is to maintain a slight upward head tilt and slightly forward head. This allows the IJV to open up a bit. The problem is, when the body is in this posture chronically and subconsciously, the wrong neck muscles are being used to support the head. The suboccipitals, SCMs, and scalenes take over, while the deep cervical anterior neck flexors get weak. Deep neck flexors are crucial muscles for cervical stability. So it is possible (obviously not all cases) that CCI that comes out of nowhere may be due to chronic muscle imbalances directly caused by the styloids. And removing the styloids is the only way to start using the correct muscles of the neck. At the very least, removing the stlyoids will open the IJVs (even if CCI is not addressed). I would have to see your CT to really know how much the styloids are contributing to things though. Obviously there are health conditions and injuries directly responsible for CCI and styloids are just the icing on the cake.
So to really answer your question, this is what I think (but I am not a doctor): removing the styloids if they are problematic (directly causing IJV compression as clearly shown on a CT) is the only way forward to really know how much of your symptoms is being caused by CCI. I would personally tackle the styloids and then see if CCI gets better with the gained proper neck range motion and physio.