Zaphod Beblebrox - I did our Airlines high altitude stall routine on both the B737-400, and the 320 series. . As a former light aircraft pilot I would say that one of the most significant issues, at least to me, is pilot stall perception. Civilian pilots who did their primary training in general aviation aircraft, Piper or Cessna or similar, are used to a definite stall break that signifies the full stall. It is easily observable and definite. I found this to be even more pronounced with aerobatic aircraft.
The B-737 simulator would stay in a stalled state with almost no break with an aft C.G. It required a forceful push and re-trim to get the nose down below the horizon and recover from the stall. The stick shaker and stall warning were going the whole time. It is easy to lose 3000 feet or more starting from 37,000. There is very little excess thrust available.
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The industry experts have said, repeatedly, that current simulator modeling does not replicate the aircraft in the real world. So believing the simulator is anything like the real world is not a realistic observation. It might be close, it might be significantly different. We just don't know.