I did sand it all the way down, but it is only veneer, and at some point I was going to sand through the veneer. The handle, a T shaped one, is of course long gone, and so I substituted two modern square ones. I will be on the look out for a 2 inch on center handle, but those are not commonly found here, and I'm not drilling anymore holes in this thing.
I spent maybe a week of spare time with this, and, it is much less ugly. I'm sad that I can't bring it all the way back. If it were going anywhere but my sewing room aka the TV room aka the guest room, then I would probably paint it Chinese red. I may, anyway, but I will leave well enough alone for now. Sometimes when I am disappointed, I make rash decisions, and so I'll see if it becomes less disappointing over time. I'll take another photo to show you the clever little chair after I reupholster the seat.