There's a previous thread about punchboards and punchboard "cards" and tickets, here:
http://www.net54baseball.com/showthread.php?t=194739
-- inconclusive, but informative.
We still think the accordion-folded cards could maybe, conceivably, possibly, perhaps,
if rolled / coiled as we earlier conjectured, have been featured in boards much less than
a full inch thick, but that's just a guess. More examples and more research required...