The CS1237-SO looks interesting.
A couple of things I spotted in the data sheet…
- REFIN specified from 1.5V to VDD
- input range (differential) specified as +-Vref/Gain
- REFIN current / resistance isn’t specified (sadly)
- PGA gain of 1,2: inputs are rail-rail
- PGA gain of 64, 128: need 0.75V headroom
You could try using the Microchip AN method, with a regulated 3.3V supply, gain of 2 and a divider resistor Ra of around 500 Ohms, I guess. That would give about 5mA drive, and <4mW dissipation in the Pt100. Not sure if that’s enough to cause trouble with self heating.
I suggest you consider using input filtering and a 4-wire measurement method - refer TI SBAA336 circuit note - to remove lead resistance errors. (The TI circuit also connects REF to the resistor, so you measure a direct ratio. But this relies on the REF input pin taking next to no current and I don’t know if that’s true for CS1237.)
If one of the force wires breaks, the voltage across the Pt100 will fall to 0V and the ADC can see that. However, if a sense wire breaks, the ADC will measure some combination of input impedance and leakage currents and that might just look like a real reading. This value is likely to change with temperature and chip to chip variation. If you could connect a 1 Meg (?) resistor between AINP and AINN then a broken sense wire would make the ADC measure near 0V again.