I think it's a bad idea at this point. But, if you really want to do so.... contact Stanford FIRST. Do know that you might actually WANT to go to Berkeley later i.e. as a professor. And, I'll tell you one thing I heard from my Berkeley professor. She actually remembered that one of the students that they tried to recruit TEN YEARS ago turned down Berkeley's offer and went to Harvard. She even commented that they were surprised that this student turned down Berkeley's offer and went to Harvard. They were like, "what?!". Now, that student is currently a Berkeley Professor. These things do happen and people remember.