To my knowledge, you've looked at the same 3 places I would have looked.
You might consider
this article in Tech Tips. On a '59 (in the same Task Force series as your '57 and my '58) there is an added location for the VIN:
on the top of the drivers side frame rail, about 4 inches forward of the steering box.
Ours, not being a '59, might not have this additional one, but it is worth a check. I've haven't looked yet to see if mine has it.
Good luck.
Bill
