Mostly Agree Mana, although the 737 at full TOGA thrust, especially at light weight, does pitch up and can be a handful. That's why there are two TOGA modes with the AT engaged. A single push of the TOGA button results in pitch and power approximating a 1500 fpm climb while a two push TOGA gives full TOGA thrust. There is a reason for that feature. You sort of said that, but kind of contradicted it in your admonishment of a post as well.
Stabilizer is the boss? Spot on!
Sciolistes,
You inquire why the path steepened but really you answered your own question at the same time. As the airspeed increased the "crossover" effect of the dominant stabilizer authority probably continued to increase thus driving the nose down more and more as AS increased. Also, I don't find it inconceivable that a very fatigued crew under certain circumstances could react this way during a TOGA.