I can't answer this for you, but the miller tables I've seen don't use slate, but use a flat, slightly porous rubber matting. I see to see this for sale at home depot, think it was the matting you'd put in a bottom of a toolbox, but haven't seen it in the hardware store recently. Others have used chalkboard spray paint on a flat aluminum surface. I think they needed to treat the aluminum with some acid first to get the roughen the surface of the aluminum up so the paint would stick and not flake off.
I had a miller table that I bought with the rubber mat I mentioned, The Black Magic company has since gone out of business. It worked with a 500 GPH 12 VDC pump hooked to a PVC adjustable valve. Whatever the smallest valves they sold at home depot. It had four adjustable legs. Perhaps you can get a pump like that and with a couple of boards at the end, run water across it and try the black sands. My gut tells me it needs to be flat and the sands would pool in the little grooves on the slate as it is now until it is planed smooth. Either that, or make it reversible by planning one side and keeping the other natural to test your results.
I wish you luck in your endevours. IME, when I try to fab something myself, it usually ends up poor quality or I spend much more than had I just bough the part.