As someone who is shy around strangers and used to have stage fright, I have a few suggestions, nothing earthshaking.
My old man made me take a speech class in high school. I hated it but it did me good, speaking to a bunch of kids who all had to do it in front of the rest of it as well. The class bonded over it and was very close. So having someone sympathetic in the crowd you can focus on helps a lot.
I did radio in college and speaking on the air to "no one" was very difficult at first. So I imagined a friend sitting on the couch and spoke as if I was talking to him. You can imagine someone in the crowd if that helps.
You needn't make eye contact at all. Just look out blankly or stare at your instrument. Everyone will think you're just a very intense musician. No worries. Hardly anyone will realize if you mess up. If the band drinks a lot, I'll bet the crowd does too.
A little fear can be your friend. It keeps you alert and avoids being complacent. Learn to make a little adrenaline and the butterflies that go with it an expected friend, not the enemy.
Lastly, and perhaps most important, there is no substitute for preparation. I lecture regularly too, and my best talks are all well practiced where I am an expert on the material. With music there is no substitute for practice.
Best of Luck
Dan aka Little Swerd