I would use the same method used in printers, 2400 dpi optical page scanners and old ST-506 stepper motor hard disk drives, which is driven by a stepper motor with enough torque and slew the arm with an acceleration profile to prevent slip. The arm must have an optical sensor for the home datum position that is convenient enough to recalibrate the stepper position in case of slip or overshoot back to "home". This is the same method used in all floppy disk and old stepper HDD actuators with 0.001" resolution. Some use micro-steps with viscous wheel dampers to maximum performance with max acceleration ramp and minimum settling time. In your case arm inertia is high on changing position with a linear actuator.
The stepper motor shaft may be a nylon cog belt or a steel foil band or chain or some other stiff flexible coupler. A viscous damper wheel with oil filled brass in a plastic wheel is a great advantage for stiff resonant actuators.
For higher torque arms, one can also consider pneumatic valves with a rotary optical encoder which offer greater speed, torque in a smaller package but more expense. The control algorithm can be tuned with temperature feedback rather than guestimated dwell times using a thermocouple feedback. then you have the optimal thermal profile and minimum time for the operation.
Self checks for sensor feedback are essential for any possible failure mode.
My guess ... you used a stepper motor with slips caused by accelerating too fast in the past. With an understanding of inertia, and motor torque and commutation rates, you can improve the performance greatly.