Very interesting laminations. They almost look like partial split planchets (if there is such an error). Keep up the hunt!
When I was a little kid in the 1960s era, I was given those fairly often in change at the candy store or the supermarket. At the same time, the same stores wouldn't accept them back when I tried to buy bubble gum or something with them. Myself and other kids in the neighborhood had a few of them. We called them broke pennies. If you worked on one with your thumbnail you could peel the lamination layer off, bend it back to it snapped off and thereby loosen up the next layer so you could repeat it again. usually about halfway through the penny it stopped peeling. We used to throw them in the corner sewer in front of 2301 at the corner of 183 St and Creston Ave. As far as I know, somewhere down there in the muck, there should still be about a dozen of those 'broken' pennies. I was 4 or 5 back then, so who knew someday broken pennies would be worth something. If my memory is right, most of the broken pennies I threw away had 1955 or 1957 date stamps.