What could he expect if he used a low noise op-amp to increase the voltage range into the adc ?
a slight improvement. His current resolution is 610nV, amplifying the input with an instrumentation amplifier may give him another bit. Even with straight 0-5V input to an ADC you will not very likely get better than 16 bits. A year or so ago, we were discussing a 24 bit A/D converter and someone went through the datasheet and did a worst case analysis on temperature, offset voltage etc and proved that the achievable precision was only 16 bits.
Again, achieveing 16 bits is pretty darn good.

Erik