I called Apple Support and have arranged to exchange the faulty band. Having no Apple Stores in New Zealand complicates matters; I have to ship the faulty band back to them in an RMA box, and they're shipping me a replacement.
I did at least manage to talk them into sending me an advance replacement, because the whole process of getting the faulty band back to them is likely to take at least 2–3 weeks based on what happened a couple years ago when I got some faulty AirPods Pros replaced.
But even as an advanced replacement, according to the order confirmation I just got the replacement band is still going to take at least another 2–3 weeks to arrive. Which means it will be, at bare minimum, over two months since I initially placed my order. And that assumes the replacement band isn't faulty, too.
I'm glad Apple was willing and able to work with me on the returns process, but I am still absolutely livid. I've owned literally dozens of Apple Watch bands over the past 10 years, and of course it would have to be the most expensive one that I've ever bought, and the one I've already had to wait on for six weeks, that turns out to be the first dud I've ever had.