You didn't understand my post. I said, "control", not support. Of course the neckstrap should take all the weight. But it doesn't "control" anything. If you don't use your head for that anchor point, your arms have to perform that task. Your jaw pushes up, gravity pushes down. You control the up forces, the universe controls the down. No teeth means you've given up half of your control. There's nothing else to steady the horn if you don't use the top of your mouth. It's all about balancing forces. And using your head is the simplest, easiest way.Instead of trying to control the whole weight of the entire horn with both hands to counter the force of your jaw try adjusting your strap then you won't be having to use your jaw.
I'd be interested in hearing your tone quality across the range of the horn using your no contact embouchure.