ORIGINAL: cutaway
....Many gliders and FF power rigs put the CG near the TE or even behind and use a heavily lifting horizontal stab to compensate.
The lifting airfoil on the tail doesn't compensate for the CG being that far back. It's the area of the stabilizer combined with a long tail moment that allows the CG to be at these extreme locations. Using a lifting section on the stabilizer just allows the tail to provide the lift it would do so anyway in a more efficient manner. The CG isn't that far aft because of the airfoil but the airfoil is shaped that way because the CG is that far back.