I learned when I was in direct sales and at such meetings to just stop talking if I was a speaker or teacher and look directly at the person(s) talking which would cause everyone to look in that direction as well and it would get the attention of the person(s) speaking to each other. Most times nothing had to be said cause the offending person(s) would get embarrassed once they realized everyone else was listening in on there conversation and they would stop.
If it did not get there attention I'd walk up towards where they were and would just stand there listening in to what they had to say as if I were a part of there conversation and they would get embarrassed and just stop.
We were taught this by a wise and smart district manager and it works.
It also would not hurt to let folks know up front what you expect from them. I'm like you I am considered somewhat abrasive to some and just say what I have to say and learning the above technique helped me alot not to offend anyone by my words but embarrass them quietly.
At our guild if we speak while someone else is everyone just tells us to be quiet. And no one seems offended since several say "everyone be quiet please".