It turns out that Google's own Data Liberation Front has a tool to accomplish just that. What you need to do is
- Download the "Escaping from Google Sites" tool.
- Double-click on the downloaded google-sites-liberation-1.0.3.jar file to run the program. If the program doesn't start up, perhaps you don't have Java installed.
- In the Host: box, leave it as sites.google.com
- In the Domain: box, fill in the domain where you have your existing Site (e.g. eipstech.com) or just the word site if you are not using Google Apps.
- In the Webspace: box, fill in the name of your Site; this should be the part of the URL after the / (e.g. if your Site's URL is http://eipstech.com/misterhay then your Site name is misterhay)
- Feel free to check the Import/Export Revisions: box if you want that.
- Username and Password should be your account information for the domain that you are trying to download from (e.g. dhay and mypassword )
- Click the Choose Target Directory button and select where you'd like the backup of your Site to be saved.
- Click the Export button, and the program will download your Site to your local computer.
Restoring your Site to your new account is the opposite of this process.
- Choose Target Directory (where you previously backed up your Site)
- Username and Password for your new school
- Webspace on the new domain where you'd like your site to be
- Domain where your new site will be
- Host is still sites.google.com
- Click the Import button, and everything should get uploaded to the new place
Hopefully that works for you, it did for me.