It seems, based on my measurements, that the MUXOUTP / ADCINP and MUXOUTN / ADCINN pins are switched in polarity in the datasheet when compared to the actual IC.
So, the MUX routes the positive input to MUXOUTN (pin 27) and the negative input to MUXOUTP (pin 24).
And the positive input of the ADC is ADCINN (pin 26) and the negative is ADCINP (pin 25).
Can someone confirm that this is in fact the case?