We are normally in Mission Bay, but I have gone down to the Big Bay and have done what you are doing now... going from free spot to free spot. When I contacted the harbor police I wasn't given any sort of permit, but was just told, "OK we've written down the info."
Just wondering, were you actually issued some piece of paper?
BTW there is also a spot in Mission Bay... Mariners Basin, that has a 72 hour limit.