Given that this is a piece of professional equipment, it only has balanced I/O... So I opted to tap straight into the unbalanced internal wiring in order to pull out a signal and ground reference that I can actually use in a normal Hi-Fi setup (in the tape loop!). Okay, I need to add a buffer stage really, but for now this works.
And I've noticed something rather odd.
The noise is gone!
It seems that the balanced input and line driver stages were responsible for the majoroty of the noise the EQ produced. When you consider how many op-amps are inside it, that's pretty impressive. So why design such a quiet EQ circuit and then ruin it with such noisy I/O stages?
Sometimes, I think I'll never understand modern manufacturing practices.