On the topic of stabilizer jack-screw speed I believe the video clip attached a few entries back is not showing the fastest available speed. 777 and 787 have stabilizer ranges of approximately 15 degrees with the maximum surface movement rate of 0.5 deg/sec. That gives 30 seconds to go from one end stop to the other. I believe that the 737 has a similar stabilizer motion range and may operate a bit slower. As a lower bound, I know that the 737 stabilizer can be moved at a rate of at least 0.25 deg/sec.
This is a slow surface and for that reason (among others) advertised piloting procedure is to always fly maneuvers and establish steady flight via the column (i.e., the elevator) using stabilizer trim only as a means of relieving steady column forces.