Whee, I found a way to make it work. I started downloading the installer in Product Manager, and then hit 'Pause'. Found where PM was downloading the files to, and copied the whole Sounds directory there from the USB stick. PM verified those files and downloaded the missing ones.
And finally the PF Installer is happily doing its thing. Thanks, Toontrack, for making the Product Manager flexible and forgiving to those who muck with its downloads-in-progress. Maybe a future version could add a "Use Local Installation Media" that could try reading locally first, and hit the internet second.
In any case, thrilled that it's finally working. Will probably copy good versions of the damaged files back onto the USB stick, in case I ever need to reinstall it.
Hope this tale is useful to anyone with a similar issue!