Seeking a plugin that shows login screen for private bbpress topics?

I have private forums via bbpress. Unfortunately, when I link people to private topics, they see a 404 page unless they login.

I have resolved this temporarily by making the 404 page explain that the content is private and show a login field, but I don’t want that information to appear for actual 404 pages.

Is there a way or a plugin that would allow me to show the login field or a custom page for topics and forums that are private in bbpress?

We use for our forum to let users create private topics and replies. Works well although you cannot make the whole forum as private.