@ Maurice
What you want to do is possible, but is definitely more complex.
To answer your question, yes, you can make the directory home page private.
On your individual pages, make sure to use the home_id shortcode option. Set it to the current page id of the page that you are using the [connections] shortcode on. It should default to the current page, but this should help ensure that. Hope that makes sense.
Now, the directory home page, you could make that private to only you or one of your groups, which ever makes sense to you. With this type of setup, the “View” links on the Connections : Manage admin page will always resolve to your directory home page. The same for the widgets in the Widget Pack. Important to know since you are segregating the directory. Off the top of my head, they is the only limitation that I can think of. Everything else should “just work”.
You can try this out with no purchases using the included templates to make sure this will meet your needs. Hope that helps!
