The thing I would like to do is get a list of the various pieces of software I've installed over and above the stock selection that ships with Edubuntu, so I can reduce the time spent redoing all that installation work. Does anyone know of a good way to get the system to tell you a list of all the .debs you have installed beyond what it shipped with?
sudo dpkg --get-selections | grep -vi kernel > installed-pkgs.txt
Backup the file, install new system then
sudo dpkg --set-selections < installed-pkgs.txt
Looks like I misunderstood the original question. The above works (but is missing a required step) but comes with a caveat, as well. This does not set the correct state of "autoinstalled" for packages that were pulled in as dependencies, meaning you will not be able to use aptitude to remove subsystems any more. Every package will be marked as explicitly installed (and thus nothing will ever be a candidate for auto-removal).
The required step is:
$ sudo apt-get dselect-upgrade
This tells the system to bring the installed set of packages into compliance with the selections you set in the earlier commands (ie; nothing will actually be installed until you run this). I'm not sure why you'd want to strip out the kernel packages, either.