I hate to burst anyone's bubble here, but fine silver, coin silver, sterling silver....they will ALL tarnish to black with time. The rate depends on the surrounding environment (especially sulfur), how much handling the silver is exposed to, etc. There are other silver alloys that will "resist" tarnishing. One has a very small amount of germanium alloyed in it and another has a couple of percent of beryllium.
And if you melt coin silver, you don't get "a slag of copper and other metals floating on top". As completely miscible alloying elements, the copper and silver cannot separate. What you get is a small amount of copper and silver oxide that form, at high temperature, with atmospheric oxygen and float on the surface. A pinch of powdered borax will gather the oxides up in a molten borax glass and leave a shining button of molten coin silver.