That sounds fun! Except for the stage fright part!
For me, the trick is to either bring sympathetic audience members, or figure out who they are very quickly. I'd stage friends in a few different places around the audience if possible, so while you're dancing or moving about the stage or just tossing your eyes around, you'll have a friendly face to lock on. Folks will be able to tell that you're making eye contact, but if you can rotate between 3-4 friends, nobody will ever know who you're looking at and you'll seem confident at the same time.
Finding the sympathetic audience members is more of public speaking tactic, and it requires a little blind faith (but it feels great once you get it right). You'd need to begin by seeing who's making eye contact with you; look for the people who seem interested and who are following along by nodding, smiling, or tracking you with their eyes. These are your engaged audience members, and they probably want you to succeed. If you can make yourself a mental map of where these people are, you'll always have a friendly face to turn to. Frequently these are the people who come up to me after a presentation to ask questions or give compliments.
I guess the motif here is that even if you're performing and you feel kind of alone, there are probably plenty of people who can help you feel successful.