I never worked for the big three , i once did an interview, with my long hair back in the days and refusing to wear a suit, it did not feel like a match ...
There are agencies that specialize in brokering freelance consultants , but it all depends on your CV , so the best thing to do is to fill it with some nice projects like the http://www.hixup.com/ you made ... , if you want to discuss in detail , mail me at HN id@gmail.com