Thanks for all the replies.
Coincidentally, I had purchased some Ammonium Persulfate when I purchased the Ferric Chloride (both from MG Chemicals). I thought it might be a cleaner alternative. But I decided to start with the Ferric Chloride, since it was already premixed. The Ammonium Persulfate comes as a crystal powder which has to be mixed. I'll try it next and see how it does. Does anyone know the proportions of powder to water (by volume) with this?
I tried electropolishing, as someone suggested. I sent a part out to ExtrudeHone to test in their "CoolPulse" system. The results didn't look any better. The ExtrudeHone rep said that to get the best results with electropolishing an "image plate" is needed - a plate that closely follows the contour of the part you're electropolishing. That makes sense, but wasn't practical in this case, which is probably why the results didn't look any better than acid soaking.
Someone suggested tumbling, which is an interesting idea. I'm not sure if that would work in this case, as the part is rather delicate. I probably gave the impression that it is some solid block of metal. It's not. It's actually a long thin ribbon (~0.030" thick and 0.5" wide) wound in a certain shape. Still, I'll probably look into than if I can't get any better results with the ammonium persulfate (or some other).
Thanks again for the suggestions. Any others are welcomed and appreciated.
Pat