Comment 4 for bug 1648278

Another workaround:
1) Boot with ubuntu-mate-amd64.iso.
2) Select "Try Ubuntu without installing" in grub. Don't press Enter.
3) Remove ubuntu-mate-amd64.iso and insert ubuntu-mate-i386.iso. Wait for a few seconds for the CD to be read; then press Enter in grub.

So we're using amd64.iso's grub to boot i386.iso.
The i386 live CD boots and /sys/firmware/efi is present, so ubiquity will know to create an efi partition etc. But there are two more bugs involved (which this report is about), which need to be worked around as well. So, from the live session and before running ubiquity:
4) sudo sed 's/-signed"/"/' -i /user/share/grub-installer/grub-installer
(so that grub-efi-amd64 is selected instead of the non-existing grub-efi-amd64-signed)
5) sudo ln -rsf /bin/true /bin/efibootvars
(so that grub-install doesn't fail when running efibootvars)

I did step (5) both in / and in /target; I'm not sure which of those two were necessary, but the system boots fine after the aforementioned steps. Of course since efivarfs isn't available, the boot order isn't customizable from within the 32bit Ubuntu.