Do you really think metal from the drain is leaching into the stone?
I never heard of that happening before. Most drains are PVC, Stainless Steel, or brass. None of those materials would leach into the stone (that I'm aware of).
For the stone in the pan shown, there is no amount of Naval Jelly or other rust removing agent that will correct Mosaico's issue. That stone needs to be replaced.
Great suggestion to make sure people to TEST first.