Thanks for giving it a shot Doug.
I do agree that the water stains do rather detract artistically. What a shame too, especially as the dark green body is so nicely marked and would prove a much more pleasing contrast to the spines and areole.
You could try cleaning a VERY small (unobtrusive) test area with a mix of 5 parts distilled water to 1 part squeezed lemon juice followed by a wash in distilled water. Hold it upside down to avoid lemon juice running into compost (make sure it doesn't fall out of pot though) and use a small watercolour brush.
You would be best to leave it till you start watering (April?).
Or alternatively, you could just say s*d it! ...and enjoy it just as it is
Bruce