Thanks Fluke (and others who posted).
I have fixed it!
After reading page 118 in the manual, which mentions the "re-centering" button (without really explaining how/when it will appear), it also occurred to me that the flashing white circle that normally surrounds the red car arrow was also missing from my 3D map screen. Although my screen didn't show
the re-centering button, I wondered if all of this "non-centered" stuff might have something to do with the behavior I was seeing.
So, I tried dragging the 3D screen around. Sure enough, the re-centering button appeared. When I pressed it, the flashing white circle reappeared and my map starting rotating properly again. Ah, relief!
Now... I still don't know how my nav system got into the state described in my initial post. I'm guessing it was in some kind of non-centered state, yet was somehow not
displaying the re-centering button. Perhaps I inadvertently dragged the display and then went about setting destinations and other things, after which the display wasn't really updating properly. I have attempted to duplicate the weird state by deliberately performing such steps, but haven't been able to.
In any case, I am glad to have normal map behavior back.