Type of stone and restoration?

Hello

Our fireplace hearth and surround is some type of gray-black stone, but is dull, very scratched and stained. It's about 50 years old, and based on some photos we took, our local granite/marble store thinks it's soapstone, and told us it would either be 3/4" or 1.5" thick. It measures 7/8"s however around the opening, and the bottom measures 1 inch. They also said there is nothing that can be done with it, as it would need to be broken up to be removed. Well, I removed one piece of the floor trim, and the slab can easily be lifted right up, as it seems the mortar or whatever has mostly crumbled. We like the idea of saving the original material. If it could be removed without breaking it apart, including the sides, could it be refinished? If it's soapstone, could it be professionally sanded/smoothed, and at least made slightly shiny/polished? It couldn't have looked this way originally. Thanks.

Crjag