I am curious how the words “polyphonic pitch shifting” are being interpreted by both the OP and Eventide. 

Well, there are different techniques one can use for pitch shifting;  this short wikipedia page gives a general overview of the different techniques:

https://en.wikipedia.org/wiki/Audio_time-scale/pitch_modification

We assumed given the example of the Pitch Fork, that what was being requested was a frequency domain, phase vocoder style pitch shifter with some improvements.

Given the fact there is a picture of an Eventide Harmonizer on that Wikipedia page, plus the fact you seem to know exaclty how the Pitch Fork works, and “polyphony” was part of an answer to numerous test questions when I was in college, I’m going to go out on a limb and trust that the small fluffy dogs know what they are doing and why they are doing it!

As an aside, it one Univibe algorithm not enough?