I stayed in Lindbergh Bay mid july on a fifty monohull last night before returning to CYOA.  Very rolly!  And short period. 
We had pulled into Honeymoon first.  It was pretty full but we did find a spot to anchor.  The place was party central with piles of people coming and going and loud music.  Not my kind of place so we moved on.  I heard from cptn Jay the the next day that this only happens about twice a year and in any case the place goes dead by seven. 
If it were me 
I would try Honeymoon.  And if that doesnt work I would use a mooring ball at CYOA before I would choose Lindbergh but of course a cat might be just fine there.  There is another option that capt 
Jay told me about - there is a bay tucked icreated/sheltered by the runway.  From what he said its pretty well protected.  Check  with Jay.