Not sure if you know, but they have 2 funding cycles every year. One during the summer, and the other during the winter, I believe. The application window for the last cycle closed a few weeks ago. If you wanted to approach them on terms outside of the usual funding cycle, I guess your best bet would be to email Paul directly.
My advice, as much as the experiences YC offers are valuable, if you've been working on a product and plan on launching it soon, I'd launch it. Sure, things might be more difficult, but generating buzz, etc., can all be done by you sans YC. It seems like some here tend to give too much attention to YC and its offerings, not realizing that most successful startups were never given a launch pad the likes of YC.
Launch and release updates often. Do some viral marketing and get in front of the face of the people you want to cover you. Don't go directly for TC, as you will spend too much time trying to get them to cover you, there are many other startup press out there will cover you with much less effort... some even let you submit your site to them :D
My advice, as much as the experiences YC offers are valuable, if you've been working on a product and plan on launching it soon, I'd launch it. Sure, things might be more difficult, but generating buzz, etc., can all be done by you sans YC. It seems like some here tend to give too much attention to YC and its offerings, not realizing that most successful startups were never given a launch pad the likes of YC.