The B737, A320 and even the Fuji FA-200 all have a noticeable negative camber on the tail-plane.
I don't think that any 'plane (except FBW high-manoeuvre military) can fly with the CG aft of the CP. There should always be a negative force on an aft-mounted tailplane, which contributes to the weight and which is why some folks prefer the canard layout in which the forward-mounted 'tail' contributes to the lift by having an upward force.
Not sure how the Avanti works it all out!