I finally got around to staining the chair and got one coat of finish on it today. I think I'm going to use a tung oil varnish for the final coats. I couldn't get it dark enough by fuming it with ammonia, probably because it was too cold outside, so I put a very dilute overcoat of LMF Nut Brown stain on it. I'm very happy with the color and appearance of it. The flecks look either dark or light depending on how the light is shining on it, much like the effect that AF has on curly maple. I was hoping for kind of a "Mission Oak" look.
Here's a couple of pictures of it. The first one is just with the fluorescent light in my kitchen, and the second one is with the flash from my camera: