OP here. Everybody take a deep breath, please.
To answer the question of why such a new bike would be in the shop, this was actually the second time I brought the bike in. The first time was for the 10-hour adjustment that the shop I bought the bike from recommends (and provides free of charge) to index the gears if any cable-stretching has happened and to make sure everything is honkey dorey. This time I brought the bike in because it had developed a creaking noise, and the cassette problem was an incidental finding that appears to be unrelated to the creaking because the creaking is timed to the pedal stroke and happens when going uphill and on the large cogs, not the small ones. (Let's leave the creaking issue for another thread, though. We're slowly working through the causes by process of elimination.)
After much back-and-forth, the LBS owner was able to convince Shimano to replace the cassette free of charge, but that offer came with a warning that "next time" it won't be covered. The LBS also replaced the chain, proactively, and without charge. The bike manufacturer was entirely and utterly useless, providing absolutely no support or help and totally disavowing any responsibility for their product, as if I had bought a bag of parts instead of an actual bike. (While the manufacturer has totally let me down, I have to say that the LBS seems to be acting in my best interest and is standing behind the product they sold me.)
Here are a few picture of what I'm told is the worn cassette. (EDIT: I'm told I can't post pictures because I don't have enough points, whatever that means. Oh well. Maybe this will work: The pictures of the cassette are at imgur.com/mQIMju9, imgur.com/bivMgRD, and imgur.com/bzKDXC5 .)
The bike still makes noise. That's next -- and not for this thread.