Well I've got a problem than I'm relatively confident can't be explained by speakers or room-response, most notably because it's intermittent.
I've had this persistent difficulty in the behavior of my gear for some time, now, and it's bad enough that non-audiophiles can hear it. I haven't been using the test-tones for long enough to say any of the following things about them, specifically, but with regular source material the problem has been...
a) unpleasant enough that my girlfriend can tell the difference
b) sometimes absent after powering-down and re-connecting everything
c) global to different source components
d) global to a different house, a friend's speakers and wall outlet
e) neither more or less likely during the day or night
f) not invokable by any known means if not already present by itself
At someone else's suggestion I just tried to run the test tone with two different pairs of speakers, and couldn't get any of the pathologies described in my OP to happen, with the original pair on which I'd been hearing all the problems yesterday.
A member of another forum also thinks that electronic explanations are unlikely, so I certainly don't mean to come across as having rejected that advice -- I just don't know how to reconcile what's been happening with any other "class" of possible explanations.