Hi,
1) Would it be possible for you to show me the hardware implementation you are using on your project (from your voltage source to your connections to the ADC pins including the potentiometer).
2) You are correct, sorry for my confusion on the number of bits for the sampleTimeNumber (I've changed the value to 7U or 3'b111 on my side for trying your code).
3) How big is the error on the accuracy of the readings you get on your ADC pins?
I've done some tests on my side (based on the project you shared, and enabling BypassCalibration and setting sampleTimeNumber to 7U) and the error I get is minimal (which is caused by the noise I mentioned on my first reply). In the following image I inserted 1.0 V to one ADC pin (that is equal to 1241 approx on the values you get from the LPC) and the other I connect it to GND; I then repeated the experiment but the other way around:

As you can see from the readings I got, the ADC value presents a small accuracy error. You can attempt to get better results if you calculate and average value from a certain amount of readings (ex: you can get the average ADC value for every 5 readings you get).
Best Regards,
Ricardo Delsordo