The first thing you should be doing is nothing (IMHO, of course), provided that the aircraft is still in normal law. The flight control law will apply full down elevator if necessary to protect the AoA.
Not true! Alpha prot is latching condition. Once alpha prot is activated if you do nothing it will maintain alpha prot by doing what ever it takes yes even climbing. In the airprox incident between A330 and A340 over the Atlantic same think happened pilot disconnected the AP but didn't break the alpha lock by pushing on the stick. The aircraft trying to maintain the alpha lock zoomed up past incoming A340. To accelerate past Alpha lock it needs to be broken by pushing forward.