You are right. The case and the movement (17J 10AN) do appear to be the same. I did find it odd that the two movements have the same date code (square shield) but the serial numbers are very far apart. Mine at 688674 and the Unknown you mention at 519735. I always assumed that the blued steel hands on mine were not original, and the unknown would appear to confirm that. The numbers on the dials are a different font, and mine has Swiss on the bottom below the sub-seconds, the Unknown does not. I doubt there is any significance, but I did notice it.
It is certainly reasonable to assume that a movement made in 1931 could easily still be available to go into a 1932 case. Having worked for a couple of manufacturers and consulted with others, I would not be shocked to learn that the Unknown with the 1931 movement and the 1936 case actually left the factory together.
I just got a new band for it and thought I'd add this pic.
