Have you ever tried using powered USB input speakers? From the description of the issue I suppose it could an interference issue as you stated. In a normal stereo system such issues are many times related to poor sheilding (cables) or a bad ground connection. I use Logitech systems on two desktops, including wireless keyboard/mouse. My speakers are powered USB input and they work very well.
I've looked for help with this issue directly with Logitech but their customer support is... not so great.
I recently switched to a desktop from my old laptop. I have a wireless keyboard (wireless solar) and mouse (M510) from Logitech that are using the same Unifying Receiver. Setpoint is installed and it works fine... until I try to connect speakers to my machine.
I originally had a set of Logitech speakers (X-140) that I had been using for a Xbox+monitor setup and figured they would be fine. Except any time I had the speakers plugged into the computer, my keyboard and mouse would stop responding for a few seconds every fifteen minutes or so. And since this is a gaming machine, that was a big deal.
Moving the speakers further away from the computer seemed to help but not by much. Eventually I replaced the speakers with cheap $15 ones and, again, it reduced the occurrence but did not resolve it.
The only time I can play anything now is by unplugging my speakers altogether and using headphones. And I hate headphones.
I really, really like my keyboard and would like to keep using it but this just has to stop. I'm open to ideas that maybe, perhaps, it isn't speaker interference but then... the problem stops when I remove them.
I have had no luck finding anyone else with this problem, though. Are there speakers out there that will not do this? Is there some other way around it?