Of course, it had to happen, didn't it? After sleeping on it, I changed my mind and decided to give upgrading the storage a go. A bit more than 2GB would be useful, after all. At worst, I'd be a few pounds out of pocket but still able to replace the original SD card.
The cheapest decent quality (SanDisk) μSD card was a trivial £6 for 32GB from Argos (we do have a Sainsbury's here, and it has an Argos inside). 32GB is a massive overkill, but hardly a problem. A quick trip into town and the hardware side is sorted.
Making an image of the old card and copying it onto the new one was, as advertised, a simple job with the suggested software.
Next was the bit that I thought might be a problem: resizing the partition on the new card. I remembered having had trouble with the suggested tool (MiniTool Partition Wizard) last year. I don't recall exactly what I wanted to do then, beyond the fact that it was something to do with upgrading my home-built desktop PC from Windows 10 to 11. Whatever I was doing wasn't available in the free version, and I'd have had to pay a vast amount of money for the Pro version to do it. It was cheaper to buy a new hard drive.
Anyway, I'm pleased to say that I had no such difficulty today: resizing a partition is available in the free version. And it was pretty simple.
I now have a working 32GB Kobo Mini.