Thanks, all. I ended up trying vinegar first without much luck. Then I tried RandallNeighbour's suggestion for the Barkeeper's Best Friend. Using a non-scratch kitchen pad, I scrubbed lightly, but vigorously for a long time, then wiped it clean, then used the vinegar again. That did a pretty good job. It's not perfect, but it's a lot better. If I decide to go for perfect, I'll give the Wurth Zebra finish a try.
