Well, if it indeed has a legit California DMV issued VIN number, then you're all set, that is the cars new registration number! The old VIN given by chrysler does you no good in tracking down the possible origin of this car!!
I still contend however, that you should be doing pencil rubbings of every number you can find on the body, getting every casting and assembly number off of the motor and trans, and every part that has a casting or part number, then do some research as to their origin! Just by the part number alone, you can tell which year, or years that the part was manufactured for! The more 1968 items the car is wearing, the more it leans to original components being used! Even if the motor is a 1971, they could've swapped all of the components from the 68 motor that was in it! If it's a 383, that's a good start right there, it could be the original, or at least lean toward the car having a big block in it to begin with!!
Plus, it's fun to trace parts on a car, like a mystery!! At least to me anyway!!! ....