I like all your terms

. Ok, we'll think about a good term to use, but since this is not a separate product or even configuration, we should be careful with new names and rather try to find a good describing attribute to attach to Workplace, such as "Workplace running in unattended mode", or Sleepless Peer/Workplace is also cool.
Back to your problem: Sorry to hear you are still having issues. One good way to narrow it down could be the following tests:
1. Can the peers A, B, C chat with each other using the Workplace Instant Messenger?
2. If you create a new space and invite A, B, C without problems?
3. If 2. works, can you check if simple business objects (Task, Note, Link) work? How about Files?
4. If you have replication issues only in certain workspaces, does nothing work, or just Files?
These are just some hints or starting points. Try such a systematic approach, which will help to isolate the problem. Anna from support will get in touch with you directly via Email and assist you with this. See also the questions that she had posted here on June 11. We'll resolve this soon, I am sure.