Why do some Mach trimmers move the elevator?
I think it's because the 9 uses free floating elevators with servo tabs to move them.  The columns just move the servo tabs which means the actual input forces are really low and there is feel spring unit in the system.   For mach trim they just have a servo motor that applies a little pull to the column via the feel spring unit, and the rod extends to tell you the motor is pulling on the column. 

There is a trimmable stab for pitch trim, but it will have a fairly primitive controller (figuring pre-microprocessor 1965 electronics) and to incorporate a mach trim mode into the stab control system was probably much more expensive than the simple setup they came up with.

The more modern setup, with hydraulic elevators that are always faired with the stab when not displaced by a control input, and a stab controller that is fully integrated into the autopilot and air data systems is way less drag.