Not to rain on anyone's parade, but this could be a nightmare for moderation. There is no way to limit a forum to invitees only, other than by removing default access by members and creating a user group for that forum and then granting additional permissions to members to give them access. It would be impossible to grant and remove permissions on a thread by thread basis because more than one thread may exist at a time. Therefore you are left with a forum on the honor system i.e. that only the invitees would post in any given thread and essentially moderation would have to remove anyone who trespasses. This is why Groups exist, but even there, participation is not limited on a thread by thread basis.