After working on another project for several months, I finally had time to return to group chat functionality. The time spent focusing on something else had really refreshed my mind. When I revisited the group chat mystery, the solution just jumped out at me.
So, group chat is now back and working very similarly to private chat. So all users have the group-related messages in their individual message paths, which means that everybody can control their own messages without touching those of other users.
Group chat is only available as a custom development. It's not part of the free version, and it's not part of the Premium version either. If you would like to use this feature, then please send me an email.