Networking with prop shops

I'm a recent grad from a target school with a mediocre GPA (3.3) in a soft major. I've been looking for a good prop shop in NYC to get trained and start my career in trading, and I've been trying to network towards that goal. Networking with prop shops is a little harder than BBs though.

-A lot of these places are small so there's very little chance that there are any alumni from your school.
-It's a lot harder to find out the names of employees and the email structure of the firms so even if you found some non-alumni people to contact, you wouldn't be able to email them.
-Because of the smaller size, sharing a group on LinkedIn is a long shot, so sometimes even that resource is exhausted.

The result is that I have to just apply and pray. Unfortunately I've never gotten lucky in anything in my life and I can't imagine my resume being picked over the 3.8 quants from MIT so I need to network. Any advice?