What I *think* I need to do is get the bootia32.efi onto the harddisk in the right place - presuming it's not already there and the issue lies elsewhere. I can't figure out a way to browse the directories or copy files to the harddisk from a live session.

The issue persists with installs of both Linux Mint Cinnamon and Lubuntu. Mint Xcfe wouldn't boot ("wrong magic number"). 2/

@Tryllesokker if the live installer isn't mounting the EFI partition automatically, you can try to do that manually:

Find the EFI partition first:

lsblk -f

or

fdisk -l

Then mount it:

sudo mkdir -p /mnt/efi
sudo mount /dev/sdXY /mnt/efi (whatever the EFI partition is)

Once it's mounted, you can browse it and drop files in - but the harder part will be getting ahold of a valid bootia32.efi. You might be able to grab it off the live USB itself (some distros include it there even if the installer doesn't deploy it) or pull it from a package like grub-efi-ia32-bin.

@jmhill thank you! I'll give that a try 🥰