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EDM is very noisy and may have voltage spikes on the "ground" 
that exceed the +-25V peak limitations of the 7I96S encoder
inputs.

Since it appears the you did not connect the grounds together there is
opportunity for these spikes to damage the 7I96 inputs. It may well be OK
but the way is was connected could not work.

I think you misunderstood the PWM output. It does no appear to be
a differential signal, so must connect to PWM --> IDX+ and GND --> GND

The frequency pin should show the current PWM frequency
The valid pin is true when the PWM frequency is above the
minimum frequency (basically a fault indication)
 

PCW,

I did that, why would it damage anything? Could a high voltage be carried through the ground wire to pin 14? This is the only thing that would make sense to me since the + wire is supposed to only be 3.3v..

Can you please explain what you mean by "Is the frequency reasonable and the valid bit set?"

Best,
-Dylan

Can you post a plot that contains the encoder velocity to determine
if LinuxCNC or the hardware is to blame?

The odd thing is that the 100 RPM plot looks to be as expected
but the 200 RPM plot is obviously broken. (the Z velocity never
reaches a steady state even though it's  obviously possible with
the acceleration constraints)

Also please use the interpolated position, the non-interpolated
position combined with the low resolution encoder makes
everything worse with it's large position steps. This is the intended
use case for interpolated position.