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.
I don't think it would work, but I'm interested to see how it would fail. It would probably lead to all sorts of weird gaming of the system ("Ebay auction for reddit account #12") and unintended consequences. But those would also be an interesting outcome of the experiment.
A simple method might be to just build on the "avg. karma" calculation that HN already does, and use that as the value of your upvotes. Have an average karma score of 3? Your upvote adds three points to the score of the post.
This is based on the assumption that people whose own contributions are high-quality are also more likely to appreciate high-quality contributions posted by others. Using cumulative karma or seniority as a basis for vote weighting would make quantity - of posts or time - equivalent to quality, and might dilute things a bit.
The drawback here is that any system of vote-weighting, when coupled with using voting to indicate agreement or disagreement, might encourage a greater level of groupthink, and leave less room for discussion of controversial topics.
That's the thing about invite-only systems, everyone assumes they're among the ones who would be invited...
Would it work better? It seems like the problem is that you get too many political submissions and polemic comments which get the votes but aren't "hacker news" in the sense of what that used to mean.
I've been here apparently 4.2 years (no idea how), and the only thing I really notice that's different is the marked uptick in political discussions as well as the more confrontational nature of commenters. Is that bad? I dunno.