My copy was the volume license edition downloaded from MS VLSC. The VLSC says there is no key required, but deploying the msi files alone via GPO results in an installation with no product key on a 60-day trial period.
I referred to the notes posted for Expression Studio 3.x. The process is basically the same but the file names have changed.
The correct key is in the WebStudioManifest.xml file, which is in the WebStudioManifest.cab file. The key is the value of the PROOFOFPURCHASE property.
Use Orca to open the Web_en.msi file and create a .mst file. Create an mst file to overwrite the exisiting PROOFOFPUCHASE value with the key found above.
Use GPO to deploy the Web_en.msi and Design_en.msi with the .mst file to change the key.