My original comment was simply to point out a current problem in this protocol design. There are some ways one can deploy to make it more difficult for Alice to send different messages to Bob and Carol without being detected, and they are deployed in Cryptocat (you're welcome to peruse the codebase and documentation.)

Just as a note, I'm sincerely discouraged from attempting to have an informative discussion with you by the fact that you keep assuming bad faith on my part, and generally responding in a needlessly rude and aggressive fashion. Consider that your general approach in this particular discussion might be why information security has a bad name as a poisonous field. If I don't reply to parts of your post, consider that it is because they are phrased in a way that assumes and implies a complete understanding, wrapped in aggression and the assumption of bad faith. I'm not here for that kind of discussion.