The overnight connection in SAN is the way to go. With an international ticket you have 24 hours to connect. No need to take the next flight. Schedule the connection for the next day. You should be able to then check bags only to SAN. In fact you probably won't be able to check them to LAX as the airline won't hold them overnight.

You can tell them that you won't take the next flight if you want. However I would not. It just raises more questions. No one will notice if you don't show however. They will certainly not hold the plane or call security. People miss flights all the time. If the airline ever inquired I'd just say that I was too late so I just drove instead. I have done this a few times and never had any issues. Personally I think the risk is so low that I'd probably do it for like a $20 fare difference.