While cruising at 390 and max weight, Being given a 70 knot instant tailwind gain, simulating jet-stream crossing, airspeed drops to alpha prot autopilot drops off.
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. Since the idea is that this happens out of the blue, you need to control the startle effect and take a moment to evaluate what's happened to the aircraft - ie, genuine jetstream, mountain wave, instrumentation problem etc etc.
Screwing around with thrust levers adds another variable to the picture which you don't need.
Only then can you make the decision to descend, and the appropriate way to do it (ie get out of alpha protection then use VS etc).