I’m assuming Dr. Kaminsky knows that your head would have needed to be in the position where you feel the dizziness most severely if he was checking for vascular compression. If he did the angiography w/ your head in a comfy neutral position, the styloid won’t be compressing the jugular or carotid & obviously blood flow isn’t disrupted. Did he, by chance, move your head into different positions during the test to see if blood flow changed in certain positions?
It may be that your styloids weren’t commented on because no one was looking at them specifically. They are often overlooked when other issues are being investigated.
You’re also right that the vagus nerve could be causing at least some of the trouble. Because it can affect blood pressure levels & low bp can cause dizziness, perhaps that’s the next thing to consider.