Can you shoot for weekday trips? Most people plan their trips for Thursday or Friday through Sunday or Monday. If you can do it, shoot for Monday through Thursday and you might be able to find some spots.
You might pick up a book on California camping that lists campgrounds - they often tell you if it's reservations or walk-in only. If so, then if you hit the walk-in only by Wednesday early, you should be able to grab a site before the weekenders get there.
The other suggestion is to check recreation.gov for availability 5-2 days before your arrival date. There might be a last minute cancellation that you can nab (but you have to have at least 2 days before your arrival to reserve online). You might also try calling the campground owners (state park office, national forest station, etc.) and asking if they have anything available last minute that you can reserve - the worst they'll do is tell you no.
1975 American Clipper RV with Dodge 360 (photo in profile)
1998 American Clipper Fold n Roll Folding Trailer
Both born in Morgan Hill, CA to Irv Perch (Daddy of the Aristocrat trailers)