Well, I don't know the exact answer to the question but I think I can make some progress. The first consideration is that most full scale airplanes are built with tail down force into the structure. With the center of lift behind the center of gravity the tail down force equalizes the torque of the center of lift, putting the center of lift on the center of gravity can cause some unwanted flying stability characteristics.

As for the inverted airfoil, a fully symetrical airfoil cannot generate lift at zero AOA, if the the AOA of the stabilator in level flight is zero then you would decrease drag. With a "negative" airfoil, the longer route for the air to travel across the curved bottom of the stabilator creates a high pressure area on the bottom of the surface and creates the needed tail-down force. A non-symetrical airfoil can create lift at zero AOA, therefore decreasing drag compared to a full symetircal. There is still drag induced by the surface creating lift but it is not as great as an AOA other than zero.

As for the LE slats, they're there to keep the stabilator from stalling during maneuvers, a pretty self explanitory theory.

-Kelly