If the platter is a simple shape without any beads, sharp edges, etc., you don't need to remount on the lathe to remove the white diamond. Put a sanding mandrel in your drill press and sand the entire piece holding it with both hands. I would try starting with 325 grit to see if that removes the white. If not, step back to 240 grit. Wet sanding with walnut oil is another option, this would be my first choice. The wet sanding has the added effect of being a grain filler, just remember to take several weeks to let the oil cure before buffing. If you don't have a drill press of sufficient size, you can put the sanding mandrel in a Jacobs chuck in the headstock of your lathe.
By the way, I would not give up on the white diamond wheel. The difference in sheen is noticeable and worth the effort.