the other reason the dental hospital may be so reluctant to give you the GA whilst pregnant is because they may not have the resources to deal with any complications.

There are lots of different combinations that can be given during surgery and the kind you are going to have for the gastroscopy still won't be a full GA. We do lists at work where an anesthetists is required and the patient receives a deeper sedation that the normal "twilight" sedation...but it's still not a full GA.