Hi! I am sorry to hear of your long wrestling match with all of this but so grateful to hear you have landed in good hands. Your questions about doing both sides at the same time given your vascular and C1 complications is prudent given my experience. Just yesterday, at my pre-op appt, I had a long conversation with my surgeon regarding the implications of tampering with C1 (i have compression on both sides as well) He voiced concern about the potential of influencing the stability of the cranio-vertebral joints there, especially if only done on one side and if there is any question of an underlying connective tissue disorder, ie: Ehlers Danlos Syndrome.
As far as the IJV approach I recently had a balloon venoplasty on the first styloidectomy side and it was immensely helpful. This was done by a NIR and my surgeon was adamant that I have the balloon vs. a stent. I am scheduled in 2 weeks for the second styloidectomy, IJV balloon venoplasty and skull base CSF leak repair.
My history is very complicated and the working theory (like it or not we are all moving in a working theory 
) is if the vascular flow is normalized by removing the styloid and balloon venoplasty this will be enough without tampering with the C1. My surgeon was also concerned about the increasing risk that comes with being under anesthesia for >3 hours.
If your team does plan on doing both sides, venoplasty of some kind and C1 it would warrant a longer stay at the hospital and the recovery may be longer as well.
You are asking all of the right questions. I would add to that list the option of intraoperative balloon vs. stent and potential of CCI with only addressing C1 on one side given the extensive fascia and ligamentous dissection that is inherent with the styloidectomy.
Sending you every good, be well!