Thought I'd announce my success.
Here's how I did it.
1. I copied the files from my Windows 7 Ultimate disk onto my computer.
2. I then removed the "ei.cfg" file from the "Sources" folder.
3. Then I followed the steps here: http://kmwoley.com/blog/?p=345
to create a bootable flash drive.
4. After the steps at that link, I just copied the files minus the "ei.cfg" file to the flash drive.
5. DO NOT BOOT FROM THE DRIVE. Open iin in "My Computer" and double click the "setup" file.
6. Install as normal.
7. At some point during the install, it will ask what version of Windows 7 you would like to install.
8. Choose the correct version that you have the key for.
9. Enter your key when it asks for it.
10. Activation is the only tricky part. You cannot activate through the internet. You have to use the phone call method.
So it works.