I've experienced high group anxiety like that - I once got off a bus in the middle of nowhere on a 4-hour trip through Central America. I could not handle being with so many people in a group setting with no way out.
I think that the build-up is something you need to work on. For example, if you were to just be walking down the street and you were asked to give some feedback to a group, you'd be fine. However, you know these meetings are coming...you know how long they will be...you feel there will be something expected of you....and you have a few days to get worked up about it.
I've been an "actor" while sober for most of my life. The one thing that allowed me to feel at ease about being myself was alcohol. I could drink, and then I didn't care about being honest and forthright.
Maybe there's something to just saying "Screw it" and not worrying about how you sound to these people? This is NOT the end of the world. There is no meteor coming down from outer space. If you stammer or stumble, people will help you, and life will go on. The kid outside will still throw a snowball at the bus when it goes by. He doesn't care what you said in group therapy and neither does 99.9999% of the universe. The only person who cares is YOU, and if YOU give yourself a break, then you'll be all in the clear!