BTW, I've since spoken with Apple Technical Support and they noted that they could hear distortion of my voice on their end of the call (I was calling using the troubled iPhone 4), but their only suggestion was to blow compressed air into the headphone port. They think that, maybe, some foreign object in the headphone port has convinced the iPhone that headphones are plugged in, when they're not, and, therefore, the when using the speaker phone, etc., the phone is try to get audio from headphones that aren't present. Unfortunately, having no compressed air available, I wasn't able to try that while they were on the phone. (And, of course, that wouldn't seem to explain the distortion of the call that they reported hearing on their end of the call, or why I can use the phone more-or-less normally when I hold it up to my head.) In any case, the only recourse they offered me was to schedule an appointment at my local Apple Store for me, which I'd already done.
Since the appointment isn't until tomorrow, and there's nothing the Apple technical support people can do to expedite handling of such matters, I have to hope that (assuming the compressed air doesn't do the trick) my local Apple store still has replacement units available tomorrow afternoon, which seems hard to believe will be the case.