I decided to alter the bootdebian script slightly, and was largely unsuccessful. The motivation for me is to run commands such as rsync (within debian) directly from the native OS. These would then be put in /etc/crontab.
chroot /mnt/debian /bin/bash -c "/root/sync.sh"
That much works fine, crontab and all. Provided that debian is mounted beforehand. This mount doesn't persist across reboots, so I added the following to fstab and unwisely typed reboot to verify that it mounted correctly. I was given a warning to the effect that I should have used "shutdown" instead, and the Kindle is now a brick. Which sucks. It gets partway through booting, and then stays on the start up screen forever. Either there's something terribly wrong in the following fstab entry, or "reboot" was a mistake, or there's a typo involved somewhere.
/mnt/us/debian.ext3 /mnt/debian ext3 loop,noatime 0 0
/proc /mnt/debian/proc none bind 0 0
/sys /mnt/debian/sys none bind 0 0
/dev /mnt/debian/dev none bind 0 0
So, as a warning to anyone similarly minded, remember to use mount -a to verify fstab entries instead of rebooting, and it might be a bad idea to call reboot from the command line in any case.
edit: Unrelated to the above, is apt-get working for other people in this thread? I couldn't get it to authenticate packages, either with the linked image or with one built from multistrap on a X86 system.