What kind of errors do you want to be able to tune out? Is it just an offset in the dry capacitance as what suggests? Or is it errors and non-linearities dependent on the amount of liquid? And/or is it errors due to manufacturing variations unit-to-unit? What is used to measure the capacitance, and what is used to output/display the data?
The general way you deal with this kind of problem is to do a calibration table for each unit, and store it in non-volatile memory of some kind. Then a microcontroller (uC) or logic device (like a CPLD or FPGA) can be used to convert the raw capacitance data to the very accurate output data.
For example, I'd bet that the delta-C per delta-V is different for the initial part of the fill and the end of the fill, versus volume changes in the middle of the fill (due to the fringe effect in the cylindrical parallel plate capacitor arrangement). That non-linearity is likely several percent, and would need to be calibrated out. The easiest way is via a digital table as I mentioned; the harder way is via analog compensation circuitry (which you wouldn't be able to tune for each production unit, for example).