FF
What you said is general principle of handling with any abnormality.
Screwing around with thrust levers adds another variable to the picture which you don't need.
The airprox incident was triggered by this very action. The A340 speed excursions were very violent fluctuating between .85 to .88. tripping the AP. The PF closed thrust disconnecting ATHR. However as you say it wasn't 200ft/mt gentle climb but despite the fact that aircaft was close to it's max it climbed at 6000ft/mt that's what triggered TCAS RA. The pilot was not aware he needs to break it by pushing forward. Once alpha prot is triggered the system may not apply full elevator or commence descent. It will maintain the alpha unless you come out of it.