mart, don't know if the 'darkening' around the nails is the same as the dark black stains radiating out from mine......some darkening I would understand but much of mine extends up to an inch or more out from them.
A customer of mine who restores musical instruments mentioned using oxalic acid to bleach, then a wash with borax and water to cleanse the area. Not sure if that would work or is safe. Whatever the solution, I can see it being a very long, tedious project.