I sort of pushed for an EGD/endoscopy, but not outright ask for it. That was my 1st time, in fact; never seen this GE before the other month (nor ANY GE). He signed me up for lots of tests, even though I was new to this whole thing. (But then, my insurance is Blue Cross, and there's never any worry about whether things can be done or not.) He knew, though we'd never met before, that I was very upset about this sudden occurrence and wanted answers more than guesswork (which we're still actually doing).
I would definitely go for the full anesthesia. If I had known that's what I would get (a co-worker told me his latest was full, but most stories I'd heard were "lightly sedated" including official literature), I wouldn't have been in such an anxious mess before the EGD. I hate vomiting, and hate messing around that gag reflex. Too many people have written that they had some difficulty (not alot) getting past it. I was so worried about the procedure itself! Then it turned out they just knocked me out! OK, that's cool!