While tracking down a wrong resistor value, noted that attaching a 68k resistor to the phantom power output instead of a 6.8k made the noise drop.

Based on the master plan, there's only 1k of input resistance in the amplifier, but 6.8k of output resistance from the phantom power.  So theoretically, all the noise inside the phantom power is amplified by 100/7.8 with no microphone connected.

Bodged on a matching amplifier to raise the input resistance to 100k.  It actually amplified the noise more.  

It actually increased the noise gain by roughly 7.1x or from roughly 100/7.8 to 100/1.  Basically, while the matching amplifier would be like a 100k resistor without an op-amp, the op-amp effectively shorts out the 6.8k, since current no longer flows through it.  The 2nd stage went from 1k + 6.8k to just 1k.

If the microphone is specced at 75ohm output resistance, it should overwhelm the noise behind the 6.8k resistor when connected.  You still need a 2x or higher stage to get more gain from the microphone.