As a simulator instructor on the 737-300 and after reading these posts I am beginning to wonder if perhaps I am teaching an incorrect technique when discussing stick shaker recovery at high altitudes. After all, we can only use the advice given in the relevant manufacturer's FCTM and sometimes that advice is quite lacking in more detail leaving it to the reader to fill in the gaps.
In the case of the 737-300 the FCTM states " Ground contact not a factor..at first indication of stall (buffet or stick shaker...apply maximum thrust, smoothly decrease the pitch attitude to approximately 5 degrees above the horizon and level the wings...as the engines accelerate, counteract the nose up pitch tendency with positive forward control column pressure and nose down trim..at altitudes above 20,000 ft pitch attitudes of less than 5 degrees may be necessary to achieve acceptable acceleration...accelerate to maneuvering speed and stop the rate of descent...correct back to target altitude.
From my observation in the simulator of high altitude stall recovery (above 31,000 ft for example) it is the application of maximum thrust that often causes a delay in early recovery because of the marked pitch up that occurs as high power cuts in. Unless the pilot accurately pins zero body attitude as the aircraft accelerates downhill, the aircraft tries to lift the nose and a "G" buffet returns. Perhaps the accent should be on instant lowering of the attitude to commence speed increase and only when at a appropriate speed above the initial buffet (say 30 knots?) thrust should increased? In the case above for training purposes, we close both thrust levers and maintain level flight while slowly decelerating towards the stick shaker speed.