How should I attach a slab of soapstone to iron shelf brackets?
Use the silicone, contrary to some ideas expressed it does stick well to clean smooth surfaces. So well, in fact, that mechanical scraping is often the only way to remove it once cured (actually there are some chemicals, like dimethyl adipate, that soften cured silicone).

If the brackets are securely mounted to the wall, silicone will grip like hell and hold that slab of stone firmly in place. Don't worry about the acetic acid, it smells a bit but won't hurt the iron. The soapstone might get discolored a bit but the underside shouldn't be a concern.