The hum problem with the Pro Channel II is caused by a small design "error" in the power supply, not something you can fix by messing around with cables, power filters or grounding. I tried all of that to no avail and realised I had to get into the circuitry and find the real cause at the source. Sure enough, it's there.
It appears that as part of the design "update" from the original Pro Channel to the Pro Channel II, two power resistors were added to the 15V section of the power supply. (The original Pro Channel uses an almost identical power supply, with the exception of an additional 150V supply added for the PCII). Those added resistors bypass the 15V regulators and allow 120 Hz ripple to get directly onto the 15V supply, causing noticeable 120 Hz hum at high gain. Pressing buttons on the EQ section can change the hum level (even with the EQ bypassed), but it will always be there.
But luckily, it's a very easy fix. You don't even have to take the board out. Just pop the top and snip the two big 47ohm/5W resistors on the pcb (R245 and R41) and it's done - hum gone and the unit is quiet even at max gain, other than some reasonable hiss you'd expect with max gain.
Actually, with that done, it's hard to find any serious fault with the PCII - it's a brilliant channel strip, especially considering the price.