Very difficult to tell what the black stuff is. In some ways it looks like excessive patina, but the stuff by Britannia's bicep looks thicker.
I would go through the same sequence, starting with warm soapy water, and if that doesn't shift it, on to Acetone. This may reveal underlying Verdigris, in which case you are onto the Sodium Sesquicarbonate or Verdicare options. I suspect nothing will shift it without taking off all the rest of the patina, turning the coin pink.
If you do get to that stage, there is a way of restoring some of the patina: if you apply a thin coat of vegetable oil and then leave the coin on a sunny windowledge the dark patina will slowly return.
Don't hold me responsible if none of this works!