Design Considerations for comparator with ~1mV accuracy?
simulate this circuit &ndash; Schematic created using CircuitLab

The classic way around this is to put a D/A converter on the ADC output, but of opposite polarity to the input. Connect the input and output together via a voltage divider, and the comparator will be looking at zero volts when the ADC output is correct. Feed the comparator with ground and the difference signal, not the two voltages. Since the comparator is always triggering at the same voltage, you can set up hysteresis easily.