Looks to me like it would be held point-down, and used to smooth some sort of soft material over a narrow flat bar. Maybe leather, as noted above. Or some type of paper, perhaps?
Some sort of burnishing tool for wood bannisters?
I will have to try this out. I will let everyone know if they can tell me what it is for sure.
This is pretty much what we have been doing up to this point, but my curiosity is just too much, and I have to know what it is.
Thanks everyone for all the great ideas. It does seem like smoothing something out is the general consensus (which was where we were leaning as well).
Cpould it be a kind-of clip on handle for removing hot trays, or something similar, from a baker’s oven (as mentioned above) or from an industrial kiln or something?
Once it clipped into place, you could probably lift a fair load with it as it’s quite a short handle.
Instinctively, from doing a fair amount of woodworking, it struck me as some sort of push stick to push specific types of wood at a mill/saw.
My first guess was that it was some kind of shingle knife.
There are such significant differences between that and what’s pictured and described in the OP that I’m wondering how one could think that.
Stick with metal thingy on end, shingle knife, same same.
It’s for shaving off a horses hoof level before shoeing the horse, I think. I can’t be certain but I’m pretty sure I saw that tool used in my childhood.
Googling on farrier’s tools and selecting “images” I see things like this, this, and these (note the hoof trim kit), but nothing that resembles the tool in the OP.
ETA: And this, from the OP’s third post: “the wear pattern is mostly on the top of the humps in the metal and not really anywhere else;” seems to argue against a hoof scraper (or shingle knife).
I have training in farriery, and I certainly never learned to use anything that looks like that. Never saw one used by any of the farriers with whom I rode, either.
I wonder if it was a specialized iron like these (used in hatmaking, etc.)?
hey, you stole my idea! 
The fact that the worn areas are on the metal part made me guess it was a latch that would be inserted into something else made of metal.
And the fact that the handle is made of wood,( which doesn’t conduct heat) makes me guess that maybe it was designed to be used as a grip for something hot.
That was my guess as well. A key to open / close the flue on an old wood burning stove or something.
It could be the lever for a rocker assembly of some sort.
I don’t think was used in any application that used blunt force, because the handle is in very good shape. is the handle threaded on or wedged in?
The metal part has a screw in the center that screws into the handle.
So the tool will be used for pushing or prying, not turning.
It’s a good thought. Old time irons were often used in pairs (or threes) so that one could be heating on the stove while the other was in use.
My thought was that it might be for radiusing wax fillets on foundry patterns.
This makes me think that it is a handle for an andiron, and the andiron proper would be the other part.
Until you find out:
“See kids, that’s the beauty of it…”