We all understand the demographic problem rather well, but IMHO any approach to fix the problem cannot occur from our activities within the site.
As users we ask questions, provide comments, ensure quality and work within the bounds of our site abilities to provide the content. We all know why most of us are here, because a lot of us are bored/angry/emotional/egotistical software developers, mostly on StackOverflow, that enjoy writing and helping others.
But this is a marketing problem and NOT a content problem!
What I mean by that is that as users we are great at generating quality site content but are limited at marketing. We can push the site on our social media pages and recommend the site to friends. StackExchange provides the tools to do just that...
How much of us are taking advantage of the social media integration tools?
A few of us likely are. Many of us may be a bit ashamed of that one rant that might get you in trouble. A lot of workplaces also monitor employee's social media and look for bad mouthing of the employer. Even if this is rare it is a real enough fear that many of us are hesitant to push the site on our social media feeds.
How can StackExchange better encourage a grass roots social media campaign?
Perhaps one area to look is what made StackOverflow such an enormous success amongst softare developers. We can say the quality controls, the peer reviewed editing model and yes these played a factor, but ultimately it was the uncanny execution of Gamification features that took the common bored software developer answering technical questions on a forum, and turned it into a competitive game.
We all know that Area 51 rewards a modest amount of reputation for emailing, or "sharing" new site proposals with people, and that sharing itself is easy on any site. The next step is finding the right competitive edge or gamification technique that will encourage a large amount of users to start advertising the site to a broader audience.
This will have a cumulative effect in that more social media buzz and hard links to Workplace will result in increased page rank through Google and Bing, thus furthering the chances that the next 10k user in the making just happens to stumble upon it and then like it enough to stay and contribute.
What else can StackExchange do?
The ball is in their court as far as I am considered. They choose to not graudate Workplace because of a problem that only they can solve at this point so they have to own this and be responsible for fixing it.