Usually we have similar uses Joep, not so much this time. I'll give you my use, in case it might be of use. I've just finished up a bit of testing on GJ System Auto Action activity posts. Can give you some general pointers/findings:
Yes posts go to the general activity stream: menu item or module. Luckily I use these for Admins only, so don't have your problem. Could you just let users have their own activity stream I wonder. I have Admin, UsergroupA and usergroupB in a group. A & B are not connected, Admin connected to both, Groups are used as kind of a collaboration area, middle ground, with profile privacy maintained. Also Admin profiles don't have activity streams, they use activity module and menu item (general), but have a comments (type) system instead on profile, maintains privacy for other users i.e. activty events of other connections.
A post by a regular user in a group, only goes to the general activity stream and their own profiles activity stream... But a user connected to all users (Admin) posts on a group wall - his post would go to all group members activity streams in their profiles where these users can comment in their own streams - but this doesn't feed back to the group wall. Yet..the stream created here allows 2 unconnected but in same group users to reply/comment to each other on the back of Admins post on Group wall, from within their own stream. Personally I love this as it solves so much for me (due to use case).
UsergroupA can create groups and events also, not B. I see this activity in general activity stream, also see when A joins a group in general stream, them joining is important for a Group, marks liftoff. Can keep an eye on this permission/power I gave them this way and know when to give a group full attention. All groups are invite.
I'd suggest, even though use cases may be vastly different, to revisit using the general stream as public or regular registered user accessible (they already have their own I imagine). Make your groups invite or approval as open is open. Visible group tabs only have 1 access level (plugin management), doesn't look like you can condition them.
Some feedback for you anyway, might give you some ideas on tackling it.
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