Coincidently I had this experience today for the first time during 3rd period class.
To get out of this, yes, it will require the iPod restore function from your 1.2.1 updater, and, yes, it may require some hefty trial and error.
(Make sure your iPod has charged up for at least 20 minutes before continuing.)
Using your links, Dr. Teeth, try holding down the center and play buttons while the CD and magnifying glass are displayed, then immediately press the left and right buttons beside the scroll wheel. You may have to do this with the iPod plugged in to your computer or an outlet, or unplugged, or stand alone.
At the same time, you want to have the software updater app open. The message should display "Plug in an iPod do update it", even though you have plugged in your iPod to your computer. This is normal, for now. When you can, hit the Restore button through the app when the iPod is registered on the desktop. Also, as a hint, look for the "Do Not Disconnect" message on the iPod.
(Those previous directions are extremely sketchy, but (A) I didn't record everything I did when trying to fix the iPod, and (B) you said, Dr. Teeth, you'd try anything. L
)
When you disconnect your iPod following the directions, the checkmark may still be present on the iPod. If so, make sure your iPod is temporarily disconnected, and quit the updater app. Then reopen the app and reconnect the iPod. The iPod should display the Apple logo and, eventually, a bar filling from left to right below that. You may have to perform an emergency restart on the iPod before you see the iPod being restored.
(If at any time you need to charge up the iPod because of possible battery life, do so via the Power Adapter for about 30 minutes. You're still going to have to complete the process, though.)
Once the bar has cleared, your iPod should work fine. Try removing it, transferring songs on it, etc. to confirm that.
NOTE: The previous data has not been officially confirmed and may not solve the problem. Also, your iPod may become very warm on the bottom. Do not worry about the heat given off.
Try it. The worst that's going to happen is your iPod will still do a scan.