I do think Win7 has something to do with it, because I did not have the problem under XP, only 2 weeks ago. The NAS drive is D-link DNS-323. What's even weirder, those clobbered filenames on the NAS are even more trouble than I thought: they cannot be renamed (read error). They can be copied back and deleted, but not renamed. The wonders!
The OS does make *some* difference at least, because in XP I could map it to a drive letter, but Windows didn't otherwise recognize or do anything about the drive. Win 7, by contrast, reports it as a NAS drive, gives it a special icon in Explorer, has a property sheet for it (though nothing about the locale) etc., so it seems to have special handling for these types of drives that XP didn't have.
I did upgrade the firmware and it seems to have helped, but this caused existing filenames to show up in wrong codepage until I reformatted the whole drive. I've had this drive for 3 years now and it seems to be reliable enough, but the transfer is darn slow, only about 10 MB per second. It'll take a day and night to put the backup back in place.
(But the firmware upgrade was a good thing - the new version finally turns off the fan when the drive is idling. Before it would only turn off the internal discs, but it's the fan that makes all the noise. The silence is welcome.)