Much more Googling around later, I found the answer: select the folder in library mode and then "Library->synchronize folder" becomes available. Voila. A bit too non-obvious. Given the complexity of Lightroom as a whole, I'm not sure I have a good suggestion for a LR fix. Perhaps looking for the issue at startup time and putting up a suggestion window? A nice, soft cudgel in other words.
If you are only getting one image fixed when using the "find missing image" option, you probably have folders that are marked as missing. Check your Folders panel. If you have any marked as missing, you need to fix this before attempting to fix any individual missing images.
As a general rule, doing a second import or a synchronize is often the wrong answer for almost all problems.
I didn't find any folder markings that looked like "!", so I looked at the thumbnails. I did not have (to my eyes) an option to say, "go look for all the missing images". I click a thumbnail and immediately I'm in the finder window looking for a single image file. If I am going to keep all my images on a network drive, I sure as heck don't want to reconnect each directory -- let alone each image. So some across remount persistency method is really needed.