Analog differential line driver and receiver circuit
No potentiometer with moving parts has any significant high-frequency output.  So, just filter the 'received' voltage.  The more important issue may be the ground
connection, the '0' volt reference level.   Are there multiple ground connections in the system?  A ground loop will pick up any local magnetic field fluctuations.

Best connection scheme for a three-terminal potentiometer uses shielded 
three-wire cable, with the shield connecting to the metal shaft and case of 
the potentiometer, and grounded in ONE place.   The three wires connect
to the potentiometer terminals, of course.   

The wiper contact of a potentiometer can be very reliable and low resistance with careful choice of materials.   The least expensive potentiometers (carbon film) are not as good as those with ceramic and conductive-plastic elements.