That's odd.
Does it do the same when you connect it to a multimeter?
- Power off or disconnected from the UHID.
- Ohms mode.
- Leads on pins 1 + 2 or 2 + 3.
An analog meter is better than a digital one for this type of test, if you can get one.

The analog meter will show variations that would be lost in the sampling loop of digital meters.
As far as substituting a lower value slide pot, that won't help.
Another thing to consider is that slider pots like this aren't designed to handle constant fast adjustments.

For a steering lever, you might try making a centering variant of the Luner Lander controller (bottom views shown) with a high reliability potentiometer like the ones used in the Star Wars yoke controller.

The shaft of the potentiometer is on the same axis of rotation as the steering handle's pivot point.
Scott