Okay, I think I figured out how to overcome my stage fright and feel more comfortable with entertaining. Once a week–eventually twice a week–I will record myself performing two songs. I will edit and post the best recordings online, so people can find them. That way, I will sort of perform in front of an audience, and I can monitor my progress from week to week. My hypothesis is this will improve my abilities by giving me weekly objectives, and I will feel less self-conscious playing in front of others after performing in front of a camera. Also, I will be able to view the performances and see what needs improvement. Wish me luck!
PS: I will post links to the videos here with written progress updates.