The dual stage comes 1st, then the single stage comes at 30 seconds.  Both were normalized & highpass filtered to eliminate construction noise.  They were on different nights with possibly different sound levels.  It was found that moving the phone & battery far away from the preamp reduced RF noise in the single stage.  This noise shouldn't be affected by the gain, though the wifi noise in the ADC is.

The lion kingdom's subjective opinion is the single stage had a lower noise floor, despite being closer to the ADC noise floor.  The datasheet for the AD8604 backs this up by claiming a 33nV noise density while the OPA227 claims a 3nV noise density.  Presumably, multiple stages of AD8604 have a significant noise increase, but the AD8604 has a real high GBWP & costs a lot.  

Otherwise, there may be a mistake in the gain calculations, since the gain with no microphone may resemble an instrumentation amplifier while the gain with a microphone may resemble dual isolated amplifiers.  Either way, the gain is more with 2 stages.