Luckily Debian isn't too hard to migrate from one machine to the other, however.

 * Installed Debian on the new machine, giving it the same hostname (samba) as the old one, but with root on LVM.
 * Ran 'dpkg --get-selections' on the old machine, feeding the output to 'dpkg --set-selections' on the new one. Installed packages.
 * Rsynced over /home
 * Rsynced /etc over to a separate directory on the new box, and copy some files (such as fstab) from the live /etc on the new box into the separate directory.
 * Rsynced /srv over
 * Rsynced /var over to a separate LVM volume.
 * Created a snapshot volume of that /var LVM volume, moved most of the live /var over to some place else, and added the original LVM volume (i.e., not the snapshot) to fstab. Obvious exceptions were such things as databases, which usually have an architecture-specific on-disk format, and the dpkg directory.
 * Brought the original system to runlevel 1.
 * Rsynced /home, /srv, and /var over again to get the last-minute changes in.
 * Rsynced (with --delete) the separate /etc over the live /etc.
 * Brought the original system down.
 * Rebooted, checked which services died because their on-disk format also differed between i386 and amd64, utterly and completely killed those, copied the files from the original amd64 /var back again, and made some type of plain-text dump that I then imported into that service.
 * Rinse, repeat until all those services work. Then, removed the /var snapshot (didn't need that backup anymore, then), and voila.