How about a turn-based strategy game where the object is to get deep enough into the singularity to upload yourself before a uFAI shows up and turns the universe into paper clips?

I don't think that would be very helpful. Advocating rationality (even through Harry Potter fanfiction) helps because people are better at thinking about the future and existential risks when they care about and understand rationality. But spreading singularity memes as a kind of literary genre won't do that. (With all due respect, your idea doesn't even make sense: I don't think "deep enough into the singularity" means anything with respect to what we actually talk about as the "singularity" here (successfully launching a Friendly singularity probably means the world is going to be remade in weeks or days or hours or minutes, and it probably means we're through with having to manually save the world from any remaining threats), and if a uFAI wants to turn the universe into paperclips, then you're screwed anyway, because the computer you just uploaded yourself into is part of the universe.)

Unfortunately, I don't think we can get people excited about bringing about a Friendly singularity by speaking honestly about how it happens purely at the object level, because what actually needs to be done is tons of math (plus some outreach and maybe paper-writing and book-writing and eventually a lot of coding). Saving the world isn't actually going to be an exciting ultimate showdown of ultimate destiny, and any marketing and publicity shouldn't be setting people up for disappointment by portraying it as such... and it should also be making it clear that even if existential risk reduction were fun and exciting, it wouldn't be something you do for yourself because it's fun and exciting, and you don't do it because you get to affiliate with smart/high-status people and/or become known as one yourself, and you don't do it because you personally want to live forever and don't care about the rest of the world, you do it because it's the right thing to do no matter how little you personally get out of it.

So we don't want to push the public further toward thinking of the singularity as a geek / sci-fi / power-fantasy / narcissistic thing (I realize some of those are automatic associations and pattern completions that people independently generate, but that's to be resisted and refuted rather than embraced). Fiction that portrays rationality as virtuous (and transparent, as in the Rationalist Fanfiction Principle) and that portrays transhumanistic protagonists that people can identify with (or at least like) is good because it makes the right methods and values salient and sympathetic and exciting. Giving people a vision of a future where humanity has gotten its shit together as a thing-to-protect is good; anything that makes AI or the Singularity or even FAI seem too much like an end in itself will probably be detrimental, especially if it is portrayed anywhere near anthropomorphically enough for it to be a protagonist or antagonist in a video game.

Maybe it would work, and maybe not, but I think that the demographic we want to reach is 4chan - teenage hackers. We need to tap into the "Dark Side" of the Cyberculture.

Only if they can be lured to the Light Side. The *chans seem rather tribal and amoral (at least the /b/s and the surrounding culture; I know that's not the entirety of the *chans, but they have the strongest influence in those circles). If the right marketing can turn them from apathetic tribalist sociopaths into altruistic globalist transhumanists, then that's great, but I wouldn't focus limited resources in that direction. Probably better to reach out to academia; at least that culture is merely inefficient rather than actively evil.