OK. I foudn the problem and feel pretty stupid. I still don't know why 7Zip won't unzip the file, but the problem was that I was selecting the folder and sending it to a compressed folder. This created a zipfile with an extra layer of directories. Instead of the template files being in the root directory of the zip file, they were in a sub directory called MyTemplate (or whatever). Oh well. The 7Zip thing was throwing me off. I think I'll quit and go home now.
"We may not be the smartest in the world, but we're the smartest you've got." -a co-worker, speaking to our manager