On rereading Don's post I realized there IS a convenient way to let Picasa do the persistent rotation: even though Picasa doesn't show you which photos are auto-rotated, *it marks those that are as edited and in need of saving, and saves the rotated version back when you press the Save button*.

Thus, when you've just added photos to Picasa, simply check whether each target folder's  Save button (in the toolbar directly above the folder) is now enabled. If it is, press it, and all photos in need of rotation will be rotated and saved that way!

There are two side effects worth noting:
- Whenever you save photos in Picasa, the originals are stored in a hidden subfolder of the folder at hand named ".picasaoriginals", taking up additional space.  Currently (v3.6), such folders must be removed manually, if desired.
- Currently (v3.6), this method quietly discards  the vendor-specific portion of the EXIF data embedded in the photo file - which one may or may not care about.