Through removing components, discovered unplugging 12V from the booster eliminated the noise.  The problem was noise in the 12V supply.  The filter capacitors are high pass filters between 12V & ground, so connecting the amplifier to ground would cause more noise than letting it float.  

A 5ohm resistor reduced the common mode noise, but suffered more differential noise of the 60 Hz variety, for some reason.  All configurations were quieter on battery power than the zillion dollar Agilent.  It definitely needs a linear regulator to drop a higher voltage to 12V like the ADC does.  A 15V battery would do the job, but cost more than a commercial preamp.  Making the booster run on 6V would be ideal.

Suspect for the Zoom H6 to have all the features it has, in such a small space, it must have extremely poor audio quality.