All I can say is good luck to you, that's not going to be easy.
I'm yet another BSME fool who did forumla sae in college (WPI) 3 years ago. I work for a company that builds CNC machines and robotics in southern NH. Which is fun, it does give me the ability to make all sorts of cool parts for the rally car.
My advice to you would be to try like hell for that internship at any of the above mentioned places, but if you're having a hard time, try and find something that will let you be hands on and creative, get a job in a machine shop or something, that experience will be INVALUABLE!!!
I know a million (ok not quite, but close) engineers who can sit in front of a computer and draw/design anything, but ask them to go into the shop to make it, forget it.
That kind of a skill will make you much more marketable as a whole because it will give you a manufacturing mindset and skills that they really don't teach you in school.
Best of luck to you...and if you happen to find that magical rally company that's hiring, please let me know!! :7 my boss is well aware of the fact that if i got a job like that i'd be gone in a heartbeat.