I never would have believed this if it hadn't actually happened.
I was trying more futile attempts last night to get my iPod to update. I restored it again; tried to add only the songs I had purchased from iTunes; tried hooking it up to a different computer. I didn't really have hope that any of these potential solutions would work, but I tried them just in case. When none of them did work, I began scouring Apple's support website and the Internet in general, looking for any solution that would allow me to get my songs on there without taking the iPod back to the store.
On the Apple iPod support discussion forum, I waded through a bunch of information that had no bearing on my issue, plus several solutions I had already tried to no avail. Finally, just as I was about to give up, I came across a simple yet unorthodox suggestion that the poster said had solved for him a number of different iPod problems. I almost dismissed it, then realized I had nothing to lose. I decided to give it a try as an absolute last resort and be prepared to just take the stupid thing back when it didn't work.
It went like this: I held the iPod in the palm of my left hand and gave it a firm, open-handed smack with my right. I then plugged it back into the dock and let it and iTunes do their thing overnight (it always takes that long to transfer so many songs, even if it only pretends to do so). I expected nothing, so imagine my surprise this morning when I removed my iPod from the dock to find that all my songs had indeed transferred.
All the trouble I went through, and fixing the damned thing was as simple as smacking it across the face. The moral of the story, I suppose, is that sometimes violence does solve your problems. I had been tempted to throw the iPod against the wall or run over it with my car, but I'm glad I tried the slightly gentler approach first. Now that it knows what happens when it gets out of line, hopefully we won't have this problem anymore.