I spent two weeks in the south of spain last month and watched much Jamon being surgically removed and while they made it look easy, I doubt that it is. clearly the knives are very sharp, but I suspect the real trick to the thinness of the slice is going in horizontally. In your picture you can see that they cut into the jamon and maintain the level. Also, it is extremely expensive, so they want it to be thin, since you have a great deal, and probably will have some left over, perhaps you don't have to be so surgical.
In any case, a great deal of envy is being sent your way from california----enjoy
Phil