I have nineteen years experience flying both turboprop and jet airliners.

In the sim, as you approach the stall you stop trimming so by the time you reach the stick shaker the airplane is out of trim and you are holding a significant amount of back pressure to keep the nose from dropping. At stick shaker you add power and freeze your pitch, as you put it, but that still requires a significant amount of back pressure on the yoke to prevent the nose from dropping which would result in an unacceptable amount of altitude loss. As the aircraft accelerates, you slowly reduce the amount of back pressure to hold the current pitch attitude.

On the accident flight the autopilot was engaged up to the stick shaker so there was no existing "back pressure" from the pilot. The aircraft had been slowing rapidly which, coupled with the relatively slow application of trim from the autopilot, would have resulted in a trim situation similar to what you have in the sim--a significant nose-down pitching tendency. When the stick shaker activated the autopilot immediately disconnected and the nose started to drop. To perform the standard sim recovery technique would require pulling the nose back up to that nose-high attitude while adding power. This is what he did, but he pulled too hard. I don't find it surprising that a pilot would pull too hard in such a situation since it's a complete surprise, not a planned maneuver as it is in the sim. Pulling too hard, and having a secondary stall indication, is a very common mistake in the simulator even though the pilot is well prepared for, and expecting, the maneuver.

The training maneuver should be changed to have a positive reduction in pitch attitude at the first indication of a stall even if that results in the loss of a few hundred feet of altitude. That is the procedure that you want to do if you ever encounter an unexpected stall warning in flight so that is how we should be trained.