I can't help you with your specific concerns but I can tell you this. I had an upper endoscopy last week during which (or before...) they gave me a shot that sort of put me to sleep. It's not real anesthesia though. I was scared to death of being put to sleep because of the vestibular problem. Looking back, I think it was mostly because I was worried that I wouldn't have control over my body so if I became dizzy, I wouldn't be able to do anything to make it stop, i.e. sit up, open my eyes, hold on to something.
Happy to report that whatever they gave me did knock me out and had zero effect on my dizziness problems. As a matter of act, I felt pretty damn good all day.
So I can't answer your questions about which type of anesthesia is best but you can probably tell your doctors in advance so that they're aware of your problems. And to back up Charlotte's experience, I had no issues with being put to sleep either. Don't worry. You'll be fine and might even be better.