You're perfectly legal. Im a cop in L.A. County, for 12 years, working patrol. Plus I'm a gun nut and I study the law.
Your shotgun is legal if it's unloaded and concealed in your vehicle. In CA, a "loaded" gun is considered loaded if a round was in the chamber OR in a magazine THAT WAS/IS ATTACHED (mag-well) TO THE GUN ITSELF.
Since your shotgun wouldn't apply to the last rule because it doesn't have a detachable magazine. That's for rifles/handguns etc...