Hi Vitruvius...
Do you have a soft-bristled
brass brush...the kind that attaches to a battery-powered dremel? If so, under running water, brush the surface of the coin with the SBBB at an angle...and ever so softly...so that the bristles are barely knocking against the coin. This should
help knock most of the dirt off and polish up what
silvering remains. Afterwards, any crud that's left can be mechanically cleaned away (carefully...you don't want to scratch off any of the remaining silver or pry up any loose
patina) with a diamond-dusted
dental pick. When all the dirt has been removed, use the SBBB again and you should have a very satisfactory piece.
If at any point you find the
silvering coming off, you may wish to stop and weigh the risks of further cleaning.
Hope this helps.
Chris