@Stavros you're welcome.
Rather than a pub with members, I would see the situation rather as a network with participants. Any participant could announce their own pub to the network as well, and then your pub is no longer a single hub for the network. But the network does remain private, limited to whomever has the cap keys.
Every participant has to edit their ~/.ssb/config
to set the cap keys, unless their SSB app has its own way to change the settings.
Another reference for use of cap keys I should have listed:
- %ZulcQJm... - @regular - using a public key as a network key