On promoting the site - some of the standard things such as Facebook Like button, Google +1, 'Tweet this' etc would help a lot I think. Really just an evolution of the Post a Link feature, and could be hidden under a 'Share this article' so it's not too visually intrusive.
A design refresh of the site would be good, personally I quite like the minimal approach but it doesn't look very attractive - unless someone knows your site already, it looks like a hobby site.
For the "landing page" for new visitors (not subscribers), i.e. default home page, it would be sensible to have some testimonials or awards so that someone who knows nothing about LWN has some "social proof" that it's a great site. A quote from Linus or other luminaries perhaps?
Linux is far more popular now than a few years back, so it should be possible to get more subscribers with a bit more focus on promotion, without changing the tone of LWN.
Maybe you could appeal to the LWN community for free/discounted help from a professional web designer/developer? I'm sure there are some out who understand the LWN ethos and could help.