I've done something similar with Sequoia Capital before. You applied with one application at their website and they forwarded it to the startups the were funding. The individual startups then contact you for an interview if your application meets their criteria.

For me personally, hearing back for an initial interview has always been the struggle. This approach broadens the reach of my application and gives me a better chance to demonstrate my skills. Once they've considered my application and contacted me, then the ball is in my court and I can scrutinize the company and culture before replying.