Well, like everything in aerospace technology, nothing works the same way in every flight regime.
Perhaps this pitch down is caused not only by lift being produced behind the aerodynamic center of the airfoil, but also in part due to the sudden increase in drag the flaps impart when they drop. Maybe if you're pulling lead like a madman, perhaps the flaps don't pitch you down as aggressively since you're pulling up on the stick.
Also for the P-51, it is to my belief that the laminar flow airfoil (which has its maximum thickness moved more aft than most airfoils at the time), the pitch down may be less obvious, especially when the CoG is far aft, such as a full rear fuel tank condition.