A group of like-minded individuals could, and have many times, do something similar. Besides the problems you listed, you also have the one we eventually ran into: stuff gets stale after awhile. You have very few new members coming in, and various rifts appear in your community where people butted heads.
I'd also like to add that while as a community we do tend to be on the elitist side, we also tend to have a strong "info should be free" side, which may conflict with closed societies like this.
I think to really succeed here, we need to keep it public, but also keep the people who have already proven to be distasteful out. That was easier back in the day when people only had one email address if they were extremely lucky. Far harder today without requiring some sort of personally identifiable information, not to mention some way of validating it.
What happened to it? Why did it die?
I've had a similar forum many years ago but haven't been able to replicate the experience since.
Another possibility is this place was created back before sites like Facebook, twitter, etc. Once social media came to prominence, some of us started communicating via other methods and we didn't check the forum as much as we used to. When your userbase is that small, it doesn't take much of a disruption to kill it.
Maybe some kind of "top 10" of HN as voted on by the "elite" - no extra, private comment area, no special form of communication, no nothing except the additional ability to contribute a vote towards a "top 10".
I'm also not really even sure such a thing is necessary. I still love HN for it's content and conversations.