I have a similar issue and, as a child, my teacher made me read sections of famous plays or poems in front of a mirror. I had to maintain eye contact with myself whilst reciting. I found it completely and utterly intolerable to see this but it was actually quite helpful. I find that i am both very aware and simultaneously not particularly aware of the extent to which my body moves. Being able to have sense of rhythm and calm with a very clear awareness and acceptance of how you are perceived is the easiest way to reduce the issue because, for me at least, it is worsened by stress.