I tend to worry about the social and emotional piece whereas the school sees this confident kid who had no problem speaking in front of the school twice and who seems very outgoing. I guess I see the vulnerabilities that others don't see.
TT, is it possible that the school is also seeing strengths that you don't see? It sounds like your dd doesn't have playmates at home, and you're her social focus by default. It can be really tough to find playmates for any kid (gifted or not) - parents and kids' schedules are busy, there isn't much time after school, whether or not other kids that your child meshes easily with are in your same neighborhood is really somewhat happenstance. We have been very lucky to have playmates very close by who our daughters bonded easily with - so they are living that typical life where they free-range between houses with same-age peers who they spend hours on end just playing with. They are also fairly close in age so that when they are home without friends, they have each other to play with. My ds, otoh, is older than my daughters, and there are no boys in our neighborhood who are anywhere near his same age, and he can get bored at home really really easily. When he was around 6 years old, he used to talk-talk-talk-talk like crazy to me, always wanting to share some interesting fact or ask really intense questions that he wanted to know the answers to right then. I think if he's simply had a playmate close by to hang out with for a few minutes here and there we wouldn't have seen so much intensity at home.
I also agree with DeeDee's suggestion to schedule a time for the performances - my daughters both like to put on performances for my dh and I (they like to dance and generally act goofy in their performances). When they are eager to perform, we ask them to do the "show" after dinner is over. They generally then go off and work on adding more things to what they want to show us... don't know if that might work for your dd or not? After dinner works as a good time for us to watch because we're tired and don't mind sitting
plus it's close enough to bedtime that when we (parents) have seen enough, we can close it out by saying it's time to get ready for bed etc.
Hang in there!
polarbear