Upgrade to High Sierra stalls/fails at “Calculating installation time“
I finally managed to resolve this problem by attempting to see if I could use MacOS Recovery to reinstall the existing OS, if this was still possible.

Recovering the existing OS seemed not to be possible, but I was able to unlock and mount the laptop's drive (which seemed to be the point where the previous OS upgrade attempt had failed) using the recovery system's Disk Utility, and then use the internet recovery option to install MacOS High Sierra via the internet. 

The installation was successful this time, the drive was converted from HFS Plus to APFS successfully, and my data was preserved.