Loosen the nut holding the toroidal and rotate it if possible. I have reduced noise in several devices using this method.
True, but not suited to mass production ;-)
It could well be the mains disturbance will not reduce much even if the transformer itself were out-boarded with extension wires, a meter away.
I think the design of this box was mostly driven by marketing considerations making as much compromises they could get away with, given the large feature set. This thing wants to be a preamp, source selector, headphone amp, streamer with storage... a full-blown control center in the "good enough" category.