Sorry to hijack!
For anyone capable of answering: How about the first week of January!? I checked the local school calendars, and Los Angeles school district calender, and the majority of the school were off for Winter Break, so I'm thinking that the park may be busy.
Certain sites say that its one of the least busiest times, while others say it's busy and avoid it.
I'm thinking of going for five days, between January 2-6th, 2012.