I know at least at Stanford, if a professor wants you in, you are in. You fill out an application as a formality, but it doesn't matter what you put on it as long as you meet the Graduate Schools minimum requirements. I personally know of a girl doing research at Stanford *after* the application deadline, a bigshot professor told her to go to the office and fill out an ap. The desk person said "sorry, the deadline is past," the student said, "but professor so-and-so told me to fill out an application." "Oh! Well here you go..."
Of course that's a private institution and Berkeley is public, but seriously, he wants you in and has money for you, your application is not perfect but pretty darn good. I wouldn't stress, apply to a few others just in case.