Hi Paul
As per my first post, I'd upgraded the software (as soon as I fitted the new card) and also tried to format the second HDD on the B2 as part of trying to get it to work, though I'd already wiped both disks on my laptop (old habits...). I didn't think formatting would work if the USB wasn't being recognised, but it seemed to go through the process (showing partitioning then formatting), though it only lasted a few seconds in total.
After asking this question, I also experienced the B2 freezing mid-track twice within a few days, with very little usage in between. I posted on this separately and Peter has picked it up as part of a wider look at freezing issues.
Peter suggested putting the old B2 SD card back in, which I did this morning, followed by a web upgrade. I then tried both my HDDs and both were recognised instantly: each time the B2 booted up, scanned the backup, then reported mass storage present on the USB socket.
So...it seems likely the new SD card had something to do with the backup HDDs not being immediately recognised. That said, I eventually managed to complete both export processes: once they started they each ran for ten hours or so, as we'd hoped following the resolution of the past export issues earlier this year. Now I need to see if the freezing issue happens again.