Pitching moment reminds me of Mach Tuck in the single seat DH Vampire Mk 30 twin boom RAAF fighter in the late Forties and early Fifties. In a dive, compressibility would occur around Mach 0.76. The RAAF version had two extra air intakes called Elephant Ears, installed aft of the cockpit which led to the RR Nene engine.
In a dive, shock waves would form over the curved intakes and destroy elevator effectiveness. The Vampire would pitch down into an almost vertical dive. There were several fatal accidents attributed to this phenomena with the pilots unable to level out before hitting the ground. A modification was introduced which changed the intakes position to under the fuselage rather than on top. In turn that caused the aircraft to pitch up during a high speed dive and which was controllable.