OK so I it turns out I'm wrong about the remote being the source of the noise. After a big session of connection tracing in the remote today, I came to the conclusion that I could just de-solder the audio wires in the remote, and see what happens.
So after doing this, the hum/buzz was still there. Further tracing showed that there is a direct connection between the headphone socket and the subwoofer enclosure and this is not an audio cable. It is probably flipping a bit in an integrated circuit inside the amp which disables the pre-amp (and as a result my previous diagnosis of the amp still being turned on when the headphones are connected is wrong).
Anyway the status therefore is that the noise is being produced within the subwoofer enclosure, not the remote. This makes it a lot harder to fix because this is where the "brains" of the amp are and there are a lot of components which could cause the problem. I still believe it's a design fault or the quality of the components used to hit their price point, but it may be beyond my abilities. I'm going to leave it a few days and see if I get inspired to keep digging.
Oh, there isomething else discovered today: when turned "off" the speakers consume 6 watts of power, and when turned "on" they consume 7 watts. This is pretty poor for standby power consumption, and does not speak well for the environment friendliness of their circuitry. By comparison, my ancient set of Altec Lansing ACS45's (the original plastic-subby version) pulls 4 watts when "off" and 8 watts when on. That's a much nicer difference in consumption - and it even has an "auto off" feature.