I just assisted in the design of a high altitude stall demonstration for a 737-800 at heavy weight (160,000 lbs.) at altitude (FL 370). We also invited test engineers as well as upset recovery experts to ensure we had constructed an accurate representation within the aerodynamic model of the level D full flight simulator we used.
As far as "learning points" as relates to the recovery:
1. At FL 370 the thrust available is approximately 10% of that available at Sea-level. Thrust will assist only marginally in the recovery, and then mostly to assure that once recovery has been effected, that airpseed can be maintained in level flight.
2. You will lose significant altitude (2500-4000 feet).
3. Once un-loaded, the jet (simulator) will continue to fly (nose-down, recommeded at least pitch to the horizon) but with very little margin (G) available. If a pilot tries to recover with a little back pressure prior to recommended recovery speed (we also use Vref 40 plus 100 knots), the jet will very quickly go back into stick shaker (very little AOA or G available for margin). The jet will "fly" un-loaded at .3 G's but pulling quickly brings it right back near approach to stall.
4. Keep the pitch attitude no higher than the horizon, assure airspeed is increasing, and do not recover for altitude until reaching nominal speed (as recommended by AFM).
5. Keep in mind that particularly with the 737-NG, you are thrust limited at altitude, and recovery to level flight below normal cruise speed could put the aircraft behind the power curve, creating more induced drag and a higher AOA than that required for normal cruise speed.
6. The primary flight control for recovery is the elevator. Most literature from in-flight upsets indicates over-aggressive inputs from pilots can induce more damage or injuries than the initial event. But the approach to stall must be recognized and recovered.
7. A full flight simulator cannot accurately replicate a full stall condition. If the simulator goes into "full stall" it is not representative of what the actual jet may do.
8. Remember, you are just "flying the simulator" not the real jet. However, such training is very beneificial to impart to pilots in training the importance of minding the jet and recognizing and avoiding these scenarios!