I'd love to get to the bottom of the origin of the set. The cards share images with the Salutations Exhibits from 1939-47. They are on paper that shows evidence of having been tightly folded and have numbers on the back [more on these below]. Here is a better view of one front:
They are not on the same paper as is on the front of the punchboard shown, though the design is the same.
Here is a small [6 x 8 x 1/2] DD board with a slip of paper I punched out of it. The paper was tightly folded into a small tubular shape as you can see from the ridges across its face. The big black number was meant to match with the three digit codes on the players depicted [this one #563 happened not to match a player; it was a losing punch]; the red numbers are the serial number of the board, so you could not stockpile old slips and switch them. I suspect that the reason there is a number on the back of my card is precisely that; it was a serial # of the board meant to tie the winning punch to the board so it could not be reused.
How thick is the punchboard with the cards depicted?