This is my own personal paranoia buster and I think it works for others, as several Ph.D. students of mine now use it too. I use it when I do lectures, especially on new turf, or in front of my peers.
There's this guy called (insert you name here, I'll use mine) Tim Morton. He happens to have the same name as you. What a strange coincidence.
Anyway, this guy Tim has a job interview. You are his curator. Your job is to get him there and curate his work.
You introduce him. You field questions for him. You enable the interviewers to have a good, workable exchange with him. You basically shepherd him in and out of the room and guide him through the interview.
If he gets attacked or misunderstood, your job is to keep the conversation fluid—don't let Tim get stuck there. Don't take the attack personally. It's about “Tim”—not little you. There's no real need to fend off hostility or get involved in arguments. Remember there's more than just Tim and the attacker in the room.
You are curating Tim. You aren't proving he's brilliant. You're simply showing people around the Tim Gallery. Chatting with them about the paintings. You are open minded, curious and welcoming. Dumb and cheerful with a bit of a sense of humor is better than sharp and deadly and joyless.
Just let people enjoy the Tim Gallery. The way they enjoy it might not be your way or you might dislike it, or it might be discrepant with others in the room—don't worry. The more people get into the exhibits in the Tim Gallery the more they might ask Tim to do a demo exhibition in their home town.