One guy from the UMD weightlifting club last semester said he did his stone loading in his garage on top of plywood. It was two or three sheets, I can't remember. They would probably do a better job of spreading the force on the ground, though they might be harder on the stone itself and would need occasional replacement.
Of course, you could also try one rubber mat on top of two sheets of wood, like a lifting platform.
And yes, I'm actually holding that handstand. Get on my level.