Sorry to revive this old thread, but I finally solved the problem.
It wasn't the RSA Duke that did it... though that is currently installed. Nor was it the balanced tonearm cable from Ikeda... though that is also currently installed. Nor was it Cardas caps on unused inputs... though those are currently installed. Nor was it cleaning contacts, though they're all cleaned. Nor was it the power transformer whine, which Jim White says is normal.
Nope, it was cable dressing at the back of the Io! Due to the Io's dual mono construction, the two phono inputs are widely spaced. With all the tonearm cables I've used, the split "Y" for the Left and Right plugs can just barely be opened widely enough to plug into the Io jacks.
This forced the tonearm cable to rest directly on top of one of the power umbilical cords to the Io power supply.
The clue came when I realized that the RF was much worse out of the left speaker, and then noticed that it was the Left tonearm cable that was resting on the power umbilical cord.
So I grabbed a stick of lead bar solder that I had in my toolchest, stuck it in between the tonearm cable and the power umbilical - and - amazingly - the RF has vanished unless you turn up the volume (nothing playing) to tortuous levels.
Next step will be to ask Jim to make me up a pair of shielded umbilicals.
I thought this might be of use to other Aesthetix owners - or anyone who has a massively high-output, all-tubed phono stage and is experiencing similar difficulties.