My training was to reduce power first, as pulling up got one closer to a stall and/or had other bad effects.
Ours too - in mountain wave for example, the power comes off...sometimes to idle thrust, then picks up again as speed reduces and stabilizes. A manual pitch up in response to an "overspeed" is a very long way from a normal, trained-and-checked SOP response, (I don't believe it occurred here). The "Overspeed Law" will pitch the aircraft up at VMO + 6kts or at MMO + M0.010 to M0.015 depending upon initial pitch attitude. The response, IIRC, is about 0.05gee - very gentle, and the power reduces; (the Autopilot does disconnect in this circumstance).
By the time your AoA "protection" triggers, you are too slow for effective nose down control authority depending upon pitch moments determined by c.g. and basic aero characteristics of the jet.
IIRC, there have been comments that elevator effectiveness was not lost entirely, nor was it entirely lost throughout the descent. The discussion on whether elevator alone, without rolling the THS towards the ND position, and including the elevator's reduced effectiveness at its full-down position, could have recovered the aircraft has been had; we'll see on Friday whether this discussion was also had by the BEA.