I tried 3 methods to run a custom script at boot time but none work

[utu]

Now I remember.

I saved update*.tar.gz in /mnt-system as an inert 'backup'.
I moved it, off-line, into /mnt-system/KNOPPIX/ and rebooted to apply it.

So, /mnt-system/KNOPPIX is probably the 'right' directory for you in applying the
update*.tar.gz idea.