Debian on USB - Make update-grub portable

I have Debian (and Windows to Go) installed on a USB disk. It's GPT formatted and boots only through UEFI. The main issue is that grub.cfg generated by update-grub (or grub-mkconfig) has a root 'hd3,gpt4' command, which causes portability issues because the USB disk can't be expected to always be hd3. Any way to make the update-grub script more portable?

Question by Dan on Super User, licensed CC BY-SA. We show a short excerpt and link to the original thread as credit.