I tried re-saving these in Photoshop. No dice - if the problem was with EXIF or other metadata in the files, a simple re-save wouldn't have changed it anyway.
My solution was to create an action that saves an image in the TIFF format, then run it as a batch action on all the images. The TIFFs were imported fine (same thing if I now converted them back to JPEG).
The funny thing is, I've imported pictures from this camera before. The only thing that's different now is that I ran the fifth 2006 Security Update just last night.