I think I should study for the SAT, because I'll only be giving up one of my summers (I can intern during my Freshman, Junior and Senior summers)
If you're a fast learner with a knack for pattern recognition, which your internship experience suggests to me that you are, mastering the SAT for you should be as simple as taking the 10 tests in the Official SAT book and going over answers and explanations with someone. That's easily achieved over a few weeks of focused work.
It seems crazy when you consider how much people freak out over it, but I'm confident this works and I encourage you to try it out.
If you have any specific questions about the SAT or the college applications process in general (something I also had a reasonable amount of success with in that I got into all 4 of the Ivies I applied to) feel free to email me.
Stanford, MIT, and the Ivies see the SAT as more of a threshold score. I.E. there's not much difference between a 2300 and a 2400. As long as you have above a certain range, you should be fine. The SAT doesn't make or break people.