Learning how to channel that 'observed nervousness' into a positive energy takes a bit of doing - you'll get there.
If you're stopping the camera every time you hit a bump, don't. Keep going and finish the piece, and then stop the camera - that 'stop and start' was always counterproductive in my experience. Another thing to do, particularly until you get a bit more settled, would be to play through each piece a couple of times in a row in a single take.
(If all else fails, pull a Glenn Gould and just hum along.)
I really hope I can do that, the way my hands start sweating just the moment the cameras roll, the biggest problem for me is that I'm facing one on one with the camera, I don't have any kind of problems performing in concerts even with cameras rolling. I just hope I somehow manage to get a hold on it.
How about covering your camera with something like a box or cover it with some cloth and leave the lens area open? so it still can take your video. Just trying to give you another solutions 🤷🏻♀️ maybe it can help you more unconscious about whereas the camera is.
How about having someone film you but not knowing when you're being filmed? That means that you may play it five times in an afternoon but not knowing when it's rolling and relaxing as well by thinking that you're just hanging there with a friend.
Looks like the rules say right (audience) side must be in view, as well as both hands - nothing I see says you can't have a few folks in the room with you and a bit of zoom on the shot to let you put the camera behind them (and up, I suspect, to get the hands clearly in shot). A small friendly audience may help, if you can swing it.
If you're stopping the camera every time you hit a bump, don't. Keep going and finish the piece, and then stop the camera - that 'stop and start' was always counterproductive in my experience. Another thing to do, particularly until you get a bit more settled, would be to play through each piece a couple of times in a row in a single take.
(If all else fails, pull a Glenn Gould and just hum along.)