I got a war nickel a while back in the shape of that 1940, I nearly would have passed it along as a really nice coin from the 70's if the reverse was not showing, the "p" gave it away Nice finds!!!
I use to not look at both sides of the nickel - especially if they appeared "new-ish." I would date check obverse or look for the distinctive mint mark on the reverse depending on how the coin landed in my hand. If the coin appeared old, I would date check it. Then, like OP, I came across a 1939 in similar condition. I decided to start checking both sides. Out of habit, I still find myself only checking the side facing up, but I'm slowly retraining myself.
The older ones have a higher relief than the modern ones; I would've pulled those out too. I used to have a really nice 1938-S that was about AU, but it was stolen when I was a kid .