Here's one. The goal would be to make a site that would never become super popular, but just have the kind of people who used reddit in the first year.
It wouldn't make sense for a startup to deliberately make something that wasn't meant to be popular. For something like this to exist it has to be done by someone doing it as a hobby.
http://www.grupl.com has the same functionality as reddit. It was started by my friend Zach and has now morphed into a facebook app. Its still small. If you post something there it will probably make the front page shortly.
This is something specialized underground forums have managed to do by using referrals. Like you said, you can't do this for a start-up but if you add members one by one, it is possible to build a concentrated community of few hundred members.
It's an excellent idea Paul. Reddit and Digg have become polluted. A fresh, simple, laid-back approach will surely be worth daily reading among a small group of followers.
It wouldn't make sense for a startup to deliberately make something that wasn't meant to be popular. For something like this to exist it has to be done by someone doing it as a hobby.