We have a documentary film in crowdfunding with indiegogo, currently 63% funded and just a few days before campaign ends, yet we intent to extend for another 15 days. We have some involvement of top billing comedians, as the doc is about Patrice O'Neal, a famous and beloved comic who died in 2011
I think Facebook ads would work for you the best. In general, Facebook ads are amazing at building awareness among key target audiences, so I'm sure it can help you achieve your goals. AdWords rely entirely on searches for different keywords, so you won't be able to run a quick campaign.
What I'd start with is using the Audience Insights tool (http://www.facebook.com/ads/audience_insights/) to find the most precise and relevant interests for the target audience. I can tell that you can use 'Patrice O'Neal' as an interest for your targeting, so that's already great. However, it's a small audience (~40k in the US), so you will need to find some additional similar interests (Facebook is telling me that 'Jim Norton' and 'Opie Radio' could be close too?).
Next, it will depend on the country where you want to do the promotion. If it's the US, your costs will be the highest - the US is the most expensive location. So you'll need to check your results by different demographics in the Ad Reports. I'd also probably go by choosing exclusively Desktop News Feed and Desktop Sidebar ad placements, as I doubt people would be actively sponsoring projects on mobile.
So that could work amazingly well to reach that audience, raise awareness, and get them to contribute.
Some additional ideas: I'd really think about whether you can produce any viral type of content. If that's a documentary, maybe you can have '10 facts no-one new about...', 'secret photos of....', 'the hidden truth of...', 'List of XY best jokes of...' (or something along those lines) and create an article on that. Then, I'd push that to StumbleUpon and Reddit, and also use their advertising platforms to promote it. They don't offer as precise targeting options as Facebook, but you never know what could catch up and spread virally.
If you'd like me to help you with Facebook ads, give me a shout and I'll be glad to assist you!