Another reply from support, telling me to try sharing the channel settings as a QR Code - which, sadly, I’d already tried, as detailed in my first post. Unsurprisingly, it does not work.
It’s very clear it’s a hardware problem at this point - and I’m about 70% sure I know which of the two is faulty.
Link to image, as apparently “you can’t embed media items in a post”.
Look at the card on the left compared to the card on the right: the sealing ring for the piezo is very clearly off-centre, and the antenna on the left is too. Dollars to doughnuts that’s the faulty one: it’s either been incorrectly assembled or damaged post-assembly, and I’m willing to bet the antenna’s not properly connected to the PCB.
Still crossing my fingers that Seeed sees fit to send out a replacement so I can test them both - happy to send whichever of the two is faulty back afterwards!