The tiny el cheapo ADC for the W is 

https://www.adafruit.com/product/1475

based on the mighty CM109 from Taiwan

http://www.hardwaresecrets.com/datasheets/CM109.pdf

It's rated for an 83dB SNR.   It wasn't a warm & fuzzy way to close this chapter, so took some more notes on the AK4524.

The AK4524 works at 3.3V, despite being rated for 5V.  The W causes a 2ms, 40mV drop every 100ms in the power supply.  The W runs on 4.2V.

The AK4524 + AD8604 preamp suck 25mA when converting.  With the AK4524 off, the analog section only uses 3.5mA.  A simple RC filter with 75R & 2000uF knocks the noise to a reasonable level while knocking the voltage from 5V to 3.2V.  A 35R + 2000F .  Being the junk circuit it is, it could just use a separate 4.2V battery for the analog section & a 4.2V battery for the W.  The W runs on 3.5V if nothing needs its USB power.

The 70R + 1470uF filter.  LTSpice says the output ripple is 5uV.

The 35R + 1470uF filter.  LTSpice says the output ripple is 1.1mV.  There were some notes about cascading filters & inductors on the goog, but this topic is where driving LCDs was 7 years ago, completely obscure.