Interesting, when I try to follow the link to the "32 bit iTunes for 64 bit systems" page in the KB/DL1784 I get this error:
We can't find the article you're looking for.
Please return to the Apple Support homepage.
One has to wonder if the "older video cards" version has gone away.
Further to my experience syncing my iPod Classic, as far as I can tell the sync actually succeeded, at least vis-a-vis my songs, an album I just added this afternoon before doing the "deep clean and reinstall" was present on the iPod, but the sync operation didn't seem to complete cleanly, since when I told iTunes to eject the iPod, I got the error message about not being able to find the disk, even though the iPod was visible to the system as a disk and none of the devices were flagged as having problems in the device manager. I just unplugged the iPod and it seemed completely happy. So something is still not right but it's working much better than it was. The acid test will be whether I can sync my OTHER iPod Classic without having to reboot the system first, and also whether when I next try to restart my system it will shut down cleanly rather than hanging trying to shut off the iPod service / driver.