If you are over 10K, and go outside 100 miles radius from your home in CA - you fall under federal rules, log book, medical exam, and CDL. I am aware that the VIN decode also tells you what GM designed the brakes to support in GVWR/GCVW, none of the light duty stuff is rated for more than 12K combined. You probably also exceeded the design tongue weight of 450lbs for the vehicle - it doesn't matter if you put a 12K hitch on a vehicle that's rated for 5K or less - you are limited to the lowest rating (think: "You are the weakest link!!!").
You are aware that a cdl isn't needed for anything under 26,001 lbs. That is the federal standard. CA is special, very special when it comes to its laws.
Ask any long haul driver and they will tell you they hate going to CA because of its outrageous laws.
As far as none of the light duty stuff is rated for more than 12k combined, you are aware that a 3500 / 350 falls in the light duty category.
If you are using your 10,001 or higher gvw for commercial purpose then you are required to comply with fmcsa rules and regulations. CDL isn't required till you hit 26,001 lbs but you are required to do medical and logs.
Light Duty Trucks
The light duty trucks comprise of commercial truck classes 1, 2 and 3. The class is determined by the GVWR of the vehicle.
Class 1 – This class of truck has a GVWR of 0 to 6,000 pounds (0 to 2,722kg).
Class 2 – This class of truck has a GVWR of 6,001 to 10,000 pounds (2,722 to 4,536 kg).
Class 3 – This class of truck has a GVWR of 10,001 to 14,000 pounds (4,536 to 6,350 kg).
Medium Duty Trucks
The medium duty trucks comprise of commercial truck classes 4, 5 and 6. The class is determined by the GVWR of the vehicle.
Class 4 – This class of truck has a GVWR of 14,001 to 16,000 pounds (6,351 to 7,257 kg).
Class 5 – This class of truck has a GVWR of 16,001 to 19,500 pounds (7,258 to 8,845 kg).
Class 6 – This class of truck has a GVWR of 19,501 to 26,000 pounds (8,846 to 11,793 kg).
Heavy Duty Trucks
The heavy duty trucks comprise of commercial truck classes 7 and 8. The class is determined by the GVWR of the vehicle. Class 7 and 8 vehicles require that the driver have a Class B CDL to operate the vehicle.
Class 7 – This class of truck has a GVWR of 26,001 to 33,000 pounds (11,794 to 14,969 kg).
Class 8 – This class of truck has a GVWR of greater than 33,001 pounds (14,969 kg), and includes all tractor trailers.