Shouldn't have anything to do with the shape of the airfoil on the tail. The efficiency of the tail airfoil in producing the download shouldn't overcome the effect on the increased download on apparent weight.
One factor could be if your tail is already almost unloaded at your nominal cg position. In which case it might be that moving the cg aft required an UPLOAD on the tail, which although it unloads the wing, the tail is less efficient than the wing, so the over aircraft lifting efficiency drops? But I didn't think the A320s had less static margin than the 330/340s, and they show a (reduced) effect, so that seems a bit unlikely.
Perhaps as the cg moves aft the FBW system becomes more active in pitch and the increased control activity creates drag which offsets the gain in trim drag? Again, it sounds a bit of a wild theory.