When I went to China last summer, I was surprised to have been issued a 60-day F visa, when before I was usually only able to obtain 30-day L visa. I wasn't sure what happened differently, although I did get my visa through a Chinese travel company here in LA (
http://www.timelyvisa.com/, if you are interested), and I went to China to attend a conference which may be why they issued me an F visa (I believe that I had actually applied for just a tourist visa).
I was in a similar situation pre-Olympics; I went to Beijing on a 30-day visa, then got in touch with one of the people who advertise visa extensions on That's Beijing. Admittedly, it was one of the sketchier moves that I have made in China - I spoke with this guy over the phone, just some random Chinese dude in his 20s, then met him at a subway station, had a coffee, handed him my passport and visa application, and we went our separate ways. Fortunately, 2 weeks later he gave me back my passport with a 90-day F visa that had been issued in Qingdao. Lots of opportunities for things to go wrong there but I was lucky and it worked out.