That was fast. Some times you really do get lucky.
The first line of /boot/grub/install.sh ends with <<EOF, and it needed to be quoted as <<"EOF". I don't know exactly how I knew to try this, must have been a faint memory of one of Old-Polack's old posts.
Anyway, it worked without a hitch. Let's hope that it stays fine. By the way, I did not edit install.sh before, so it appears to be a bug that hasn't surfaced until now.