Around 1955 GM started adding the long VIN numbers to the frames and cabs. Before that, the engine serial number was used. With out original engine, you are at the mercy of the DMV and Highway Patrol inspection center. The numbers on the cab indicate build number, size, and factory location, nothing to do with the VIN, unless someone at one time wrote the build number in for the VIN, all the states didn't work the same.

Take the original block with you if you still have it.

Joe