Sorry man. The UCSF thing this year seemed out of whack. Most people usually just got the date that was less desired (the 12th). And I don't think they sent out more emails than interview spots. How did you not get a spot when they originally sent out the email?
Last I "heard" they were having problems filling the date on the 12th. If you call Monica/Delphaen, you should be able to find some way to come on the 12th. If you're looking at the later date, you could probably kiss that one goodbye. I think only one other program interviews that date, and so UCSF is going to have a stronghold on it.
Good Luck.