The thickness of the ground plane is going to be largely irrelevant. Assuming the ground plane is non-ferrous eg copper, brass, aluminium etc, the skin depth is going to limit the usable thickness dramatically. For copper the skin depth is about 9mm at 50Hz. Scale by the square root of frequency. Two decades of frequency gives one decade of resistance change.
Metals other than copper will give the same order of magnitude of skin depth. What you need is a large area of ground plane under the monopole. I would say a radius equal to the monopole height would be a minimum, and maybe 3x the radius would give as much benefit as you could get.
