Fluent speakers talk on regular sized exhales. A big deep breath actually almost always reinforces the feeling of panic, which is why it doesn’t work. Instead, when you feel out of air, realize what you are feeling is actually mostly fear, and instead exhale. It seems countering, but it will release the panic response. Practice alone if you can, bc it’s a bit scarier at first. Also, look into the role valsalva maneuver has in stuttering.