The stamps are mine, not images from the Internet. The collection whence I found them was mostly U.S., Pacific Islands and South East Asia and formed in the 1930s and 1940s.
A photo of the reverse shows the gum remaining, as well as a better view of the perforations. Clearly, the front, back and sides are all quite primitive; crude is such an ugly word. As for the potato theory, I can neither confirm nor deny. But if true, said spud is long gone.