There are others more knowledgable (and some of them may also even be typing right now), but...
I'm suspicious of the "switcher". It seems like there are devices out there that somehow maintain a more benign load under such circumstances (Niles audio perhaps?).
Absent that, I'd try using that Denon to power the other zones - you may be able to feed the line in of the Denon with the line out from the Yamaha if there is not a more elegant solution. I'll bet that even if you power one other zone with the Denon, you'll solve the problem. I don't think you need a big, new, expensive amp to fix this problem. But then, I'm a cheapskate.
