and welcome to the Forums!
I suspect there are a number of concurring causes to your problem…and some obscure details in your email.
-are you connecting the 3 mics directly to the H8000FW? You should not do this.
The Eventide should get the mics signal after 3 dedicated preamps or from the channels Aux Sends of a mixer to which the mics are connected.
-the 3 mics require using a preset with 3 separate pitch shifting channels, one for each mic.
3 physical inputs on the unit should be connected to the 3 mic feeds (as described above).
Please describe connections and preset name and number you are using.
-pitch shifting requires:
1) strictly monophonic signal (vs. polyphonic). The 3 mics should not be processed by the same pitch shifter. One mic > one pitch shifter.
2) a hefty input level! The H8000 has Pre A/D gains you can use to help input levels. These are under the LEVELS key. Make sure the signal lights up 4 or 5 leds on the front panel readout.
-diatonic pitch shifting requires you set the tonic and the scale in which the song is composed and played. Any change of root/key should be reflected in the settings.
If you are getting detuned notes it's because the input note *is* out of tune and/or because of the points described above and below. You can try setting the quant(ize) parameter to 100% to pitch correct input notes to the nearest scale step.
-good pitch shifting also requires you set the lownote parameter (under CAL(ibration) menu) to the lowest note the unit should expect to hear from the source. For instance a guitar requires an E2 or D2 to work fine. Check the vocal part for its lowest note.
-as for audio source bleeding into mics…I'm afraid there is not much to do, other than using ear monitoring (this avoid using stage monitors) and plexiglass panels to separate sources.
all the best