I'm going to take a bit of a different tact than just saying "here's how to do it".
The important thing may be "are you sure you're ready"??
You've been working hard, you're excited, but where are you really at? Have you gone through beta? Have you got some users? Have you gotten the feedback, is your messaging set?
I think you'll have a real challenge getting into the major tech blogs before you've got a social network with activity, and the activity you get from the publicity might not help your business to grow in the long run.
Specifically for a social network, if you get on TC and you have a social network without activity and content, you're not going to get very far.
My advice, is get out there and build the base. Make sure you've got the right amount of activity (you define that), find out what parts of your business are really resonating with people, and figure out the message/soundbite that makes a difference. When a few pieces fall together, you'll know, because writing to the tech blogs will be a piece of cake when you say "[original angle that resonates with users] provides [x]% growth over the last [x] time period" or something along those lines. That actually isn't catchy enough.
Another tactic is to not go directly for the big blogs. I got covered by a bunch of smaller blogs, and that's where TC and TechRadar found out about my site.
Another way is for you to basically write the article for the blogs, and let them basically edit it for print. The more work you do for the writer, the more likely they are to just do a quick edit and then post it. I haven't done this myself ,but I've heard of it done.
If you want to get some PR, you can also write an article about your industry which is not directly about your business. You'll see lots of these articles on TC. This may drive some people to check out your site, and help it to grow, even though you won't have your name in lights.