Sticking the blank to a small block of wood with strong double-sided tape makes it a lot easier to hold when sanding it thinner.

McCreed, can you confirm what units your additional .010 is? I assume you are measuring in inches rather than mm or cm. Also, if that 0.010” (height of a top E string) is a rough string slot depth line, then the rough top of the nut would be the height of your preferred bottom E string (say 0.042” or 0.046”) above that line.