Jim,
California requires titles, no matter how old the vehicle is.
I know it would be a little extra work, but why not assemble the rear axle assembly put the engine and gearbox in the engine bay and make it look complete. I'm not familiar at all with the rules on this (nor have I ever heard of such a thing), but I would think having all the body parts on and the running gear installed would qualify as a complete car. It'll surely be less work than dealing with the bureaucracy. I'm sure all of that could be accomplished in less than a day. You going to have any help along with you?