May I recommend the following? (I know it doesn't really address the issue of how the GA acted):

If you're on the FC waitlist, seated in coach, and someone else shows up with your seat assignment, you know you've been upgraded. If you have a mobile boarding pass (as did the OP), then presumably you have access to the mobile website, if not the iPhone or Android United app. In that case, simply refresh the FC standby list in the app and you'll see your name along with your new seat assignment in F. Simply go to your new seat and sit down. No need to wait for the GA to bring your new boarding pass. It may cause a bit of confusion when they try to find you, but at least you won't have to stand around for 20 minutes.