Fully agree with those pointing to "man-machine" interaction problems and too much relying on automation.
Since they were at about 1500 ft (450 m) altitude, why not to manually transit to horizontal flight (no problem to lose some 50 m more) and then slowly change to the desired (or prescribed) altitude. Again, slowly and without reaching high (and stressing) pitch angles. It was not, say, Heathrow, neither Schiphol with heavy traffic, hardly a couple of other planes in the airport airspace. Also, no mountains around to climb as fast as possible.