I was hoping it would be something like a USB device conflict, but now the shuffle is the only thing connected...
This article was one of the ones you linked to above in your initial post
Under Part 9. Verify that USB drivers are installed, did you try the steps in If only "Unknown Device" appears? That appears to be your situation.
Also, you said that the shuffle initially worked well enough to do a sync, then it had the same problem again. If you can get it to work again initially, before doing anything else, try the following. Select the shuffle in the iTunes sidebar, under DEVICES. Over to the right, go to the Summary tab. By default, the checkbox for Enable disk use should be unchecked. If so, check it and Apply the change. See if that makes any difference.
(If Enable disk use was already checked, try unchecking it and Apply the change. Basically, set it the "other way" and see if there is any improvement.)
NOTE: When disk use is enabled, you have to eject the iPod in iTunes before disconnecting it physically.
If the disk use change makes a difference, that may provide a clue about the actual cause.
So changing the Enable disk use setting (suggested in my previous reply) did not make any difference? (Assuming you can get it to work initially to change that setting.)
Can you list all the computers (type and OS) that you have tried this on? If it does not work on two or more significantly different PCs, it may be a defective shuffle.
If you have an Apple Store nearby, you can make a reservation at the Genius Bar. If one of your PCs is a laptop, you may want to bring it along. If the shuffle works with their machine but not with your laptop, maybe they can figure out why... If the shuffle is defective, you can see about getting it replaced.
If this is a recent purchase, you can also contact the "official" Apple tech support directly, through the Contact Us link at the bottom right corner of this web page.