I finally obtained a cable, which allows me to connect the Eventide with the system as I did it back in the days, where no noises could be heard at all (at least not that I remember).
Which means basically…
Eventide -> Mixer -> Headphones.
In the end, there's no further amplification – just the Eventide, but hey, the noises are still there.
That way, I have to admit defeat and the machine needs servicing, which is… oh god… noooooooooooo!
At least the speakers aren't at fault.