If you get past the resume screening stage (which it sounds like you'll have no trouble doing, with your resume), then those four companies you mentioned only care about your interview performance. You're correct that side projects won't get you a job at Palantir. What you should do is practice, practice, practice technical interview questions. Get Cracking the Coding interview and do every problem.

Getting a job / internship offer at those four companies is the exception, rather than the rule, so don't feel bad about getting unlucky this year. I squeaked by Facebook intern interviews, but was rejected from Dropbox, Google, and Palantir.

Better luck next year!