Thank you for the suggestion. I have not, because I did not know it was necessary. I will try that shortly and report back.
Okay, I rebooted, launched Media Center, and attempted to Run Auto-Import Now again. Again, same results, 239 files skipped.
I then went to Options yet again to look at the Support Long File Names preference. The box was still ticked. HOWEVER, when I attempted to close the Options dialog, I was prompted to saved changed settings. Which made no sense, since I did not change any settings while in the Options dialog. But nevertheless, I clicked OK to save changes, and performed Run Auto-Import Now once more time. This time, all files were imported with no skipped files!
This is very strange. I ticked the Support Long File Names checkbox at least a half dozen system restarts ago. Every time I looked at that value in the intervening (probably a least a dozen times), the box was ticked. So apparently Media Center was persisting that setting value the whole time. Why, out-of-the-blue, would I suddenly be prompted to save save changes in a dialog in which I had made no changes during the current session? To me, it appears as though Media Center was persisting the unsaved change through multiple cycles of both the machine and Media Center itself, and after the latest system restart finally decided to flag that setting as a changed value that needed to be saved (or discarded).
So rather than anything being amiss in the file importing code, it seems to me the problem may lay in the code that controls persistence of changes in the Options dialog. Just speculation, of course, but it's the only scenario that potentially explains the behavior I've seen. Anyway, as a software developer myself, that's where I would start looking. But for the moment, I'm just pleased I no longer have any import errors.
Thanks to all who offered suggestions.