In home depot or the like in the caulking aisle there should be a product for softening and removing silicone RTV. I believe its an acid based gel. Anyway, scrape most of it off and then apply with a brush and you can scrub the softened RTV off.
Why not use a clear RTV? Also, didn't they use tar originally to seal? My guess is that the silicone RTV isn't adhering to surfaces that the tar was used on. My suggestions are to add a new glass bottom on top of the slate (put a layer of foam or other support to fill the gaps between the glass and slate so they can share load). Alternatively you can chemically treat the slate to remove any hydrocarbons left over... maybe a chlorinated hydrocarbon like brake cleaner would work. You could sand the slate to expose fresh slate, and then silicone to that. Regardless of what you do I'd get some epoxy (like fiberglass resin) and paint the slate with that. That will both seal the slate and provide a surface for the silicone to adhere to.
Why not use a clear RTV? Also, didn't they use tar originally to seal? My guess is that the silicone RTV isn't adhering to surfaces that the tar was used on. My suggestions are to add a new glass bottom on top of the slate (put a layer of foam or other support to fill the gaps between the glass and slate so they can share load). Alternatively you can chemically treat the slate to remove any hydrocarbons left over... maybe a chlorinated hydrocarbon like brake cleaner would work. You could sand the slate to expose fresh slate, and then silicone to that. Regardless of what you do I'd get some epoxy (like fiberglass resin) and paint the slate with that. That will both seal the slate and provide a surface for the silicone to adhere to.