My apologies folks! I had figured this one as solved as it was going to get and forgot to watch the thread. (blush)
Since there are still some doubts, I've cleaned this up a bit more and took some new pictures. Hopefully, the new information will define this one more completely.
First of all, there was a scratched edge on it that I hadn't noticed before. It seems to confirm my suspicion that it's brass. At least, the shiny part is yellow.
Also, if you see it in person, it's easy to see that there is a sort of flattened spot on the flange. It's hard for me to get it to show up on my poor camera. Where the light is shining brightest, is the spot. I don't know if it's by design or had just been stepped on.


This is a close up of the little hole in it.
And this is a view of the very top.
This, is a view looking up into the piece from the bottom. Unless my eyes deceive me, that looks like a piece of iron rust up in the very center.
And, finally, hopefully, the most useful piece of identification I found was a mark on the side. I'm guessing it is a maker's mark as it's only on one place and not like it's part of a design. I only found it after toothpicking some corrosion off the spot.
My thanks to all the people who have taken time from their busy lives to figure this out! It is appreciated!
Happy New Year!