change potentiometer threshold

I have a potentiometer that starts at 6k ohms then sweeps up to 10k ohms, I am needing it to control a motorized actuator that uses a 0 ohm to 10k ohm potentiometer, the actuator uses a comparator circuit where the actuator position is controlled relative to the position of the potentiometer, I cannot just replace the 6-10k ohm potentiometer because it is a special style, almost like a tube, and is attached to a board with components in the center of it, is there a device available or circuit that could be built to accommodate this? if not a solution for that, is there a circuit or device available that would allow me to control a servo position with a 6-10k ohm potentiometer that I could then physically mount the 0-10k ohm potentiometer to the servo so the servo would spin it? any input is much appreciated thanks!