[PC/SR]

Dealing with Calif DMV and the CHP worked out for me because the CHP guy liked old cars and was much more interested in talking about the car than in doing the paperwork so he OKed it with just making a new registration plate he rivited on. I had no paper whatsoever to start with.
However, Slowplane's advice to get a DMV service assistant is good advice if things go sideways. They are usually former DMV employees and know the rules and procedures better that you ever will.
I suggest you let the CHP guy look at it and see what he does. It might work out. If not, search the web for a Service in SoCal.
Just remember that they want the registration money so ultimately it can be done.