A year and a half later, the mystery is accidentally solved...
I was inspired by a mystery item that I dug (see
here) that turned out to be part of a coffee grinder, and I bought an antique grinder that matched that part (see
here). I've ground coffee with it a couple of times mostly just to see that it works, but it doesn't taste right so I decided to see if it would come apart so I could clean it. Lo and behold, it disassembles quite easily, and answers what the item in this thread really is.
Here it is disassembled, with a closer view of the item in the upper left. Click to enlarge.
That part is a match to the item in this thread, so now we know the answer. It's the bottom bearing...