Solution 1:

Installing from the .msi files is not supported. It just plain doesn't work.

You have to install from a startup script (or logon script, but that's generally a bad idea). You'll want to write the startup script such that it checks for a previous installation.

Also, it's the exact same process for Office 2010. And you can do some fun stuff like dumping Office, Visio, Project, and Sharepoint Designer all into one installation folder (still have to call setup for each individually, but saves on space)

Solution 2:

I don't believe that deploying Office 2013 via GPO Software Installation is a supported method of deploying it. Here's a link to deploying it via computer startup scripts:

http://technet.microsoft.com/en-us/library/ff602181.aspx