Feedback requested on a method of posting a message without revealing the author
So a fundamental property of  multi-party anonymous systems is you are only anonymous out of the number of honest participants in the system. If the Stasi control everyone else at the dinner table and know they didn't send the message, then they know you did no matter what protocol you use.

In your case with this ring topology, because only your two adjacent neighbors  in the group know about you and therefore you only interact with them, they only need to be malicious. Specifically, if the member's before and after you collude by cutting you out of the real network and putting you in one that just involves the two of them, then they will know you sent the message when you complete the protocol and remove your key.