How to book out camping site near sykes hot springs, big sur?

I am going to big sur in a couple of weeks and trying to book out camping. it seems like all the big ones (pfeiffer, big sur campgrounds, etc.) are all booked out, but saw there seem to be some awesome hot springs there too. I read there were three different campgrounds along the 10 mile trail (barlow flats, terrace creek, and sykes campgrounds) but I'm wondering if they might be all booked out, and how I might be able to book them. The last thing I'd want is to hike in 5 miles with a heavy pack just to find that all the campground spots are taken. Can someone please help?