737er,
Also, I don't find it inconceivable that a very fatigued crew under certain circumstances could react this way during a TOGA.
No, it is not inconceivable. But this appears to have happened at the end of a what, by profile and speed, appeared to be an adequately executed missed approach. Long after the TOGA button was pressed and after the acceleration phase was complete or near the end of that phase. So it is inconceivable that they managed to control the aircraft at the critical point and end up with such an extreme and sudden nose over when the aircraft was what appears to be, completely stable.