Hi,
I think your configuration doesn´t make sense.
* You say: "I am proposing to pass the -5v rail voltage to the negative AD input"
* and then you say: "Now, relative to ground, this may mean that there will sometimes be a negative voltage applied to the positive input (unless I apply bias which would be a pity since it then cuts my dynamic range)."
If you put -5V to the inverting input of the ADC..
* then your input is referenced to this -5V and not to GND (besides -5V to -IN is not allowed)
And since the differential input is +/-5V --> this means the decodeable input range at the IN+ is -10V...0V (still not allowed)
I assume your Ion-Cell generates currents in one direction only. If so, then choose an ADC with unipolar decoding.
Klaus