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.