Tom,
Can you post the circuitry? It was a little hard to digest for me mentally, my transistor theory is a bit rusty.
I did post the pdf, but attached is a zip file with the Eagle files. Note that this was implemented on a PCB with another circuit so the PCB dimensions are about 2X the size needed for the liquid level sensor.
One of the biggest prolems with arduino's is the measurement of resistive sensors. It's nearly impossible to use the full range of the ADC. This results in very poor resolution that requires a ton of filtering to account for. In low power scenarios that filtering is expensive.
If I'm understanding the way your setup works it sounds like am amazing way to measure any resistive element (photo resistor, thermistor, etc) at a high resolution and at low power.
You are right, if you don't use the ARef input, it is very difficult to get a full range reading and, given the relatively low input resistance of ARef pin, you need the voltage follower Op Amp for any circuit with any appreciable source resistance.
The circuit will do as you say, if you put a fixed resistor that matches your highest resistance of your sensor in the reference leg, then you will get a reading proportional to the sensor resistor value. Bear in mind that this is not perfect. The current mirror's gain will vary with temperature and definitely will not track if the temperature is different at each junction. Also, if there is any variation between the two transistors in doping or area the gains will be different and you will not get a true current mirror. Fortunately, this device being monolithic reduces the sensitivity to these issues somewhat. The spec has a surprisingly large mismatch, but I have found the device matches well enough for this application. YMMV...
Alternative circuits include creating a wheatstone bridge of the reference and sensor resistors, but then you'll need a decent differential amplifier with calibrated gains and offsets (at least 3 op amps and a pile of resistors).
Tom