If you were to see Dr. Costantino, I recall he’ll do a virtual initial consult so you wouldn’t have to travel to see him up front. I assume if he agrees to do surgery for you, you would need to travel to see him at least the day before surgery for a pre-op appt. & then either stay a few days or travel back for a post op appt. I’m not sure what his protocol is after surgery. He does remove the posterior digastric muscle in cases of IJV compression, but it’s not in the neck, plus C1 gets a bit shaved off. Here’s a picture of it so you can see the location of the posterior digastric:
Racing heart isn’t necessarily a vascular compression symptom. I had that due to low blood pressure when I exercised, & it was caused by my vagus nerve. It stopped after my styloid was shortened.
Can you post a picture of your neck to point out where it’s uneven. That might help to the answer the question of what muscle was cut.