We haven't solved the problem yet so for now there will have to be a temporary solution.
If we figure this one out I'll report back. In the meantime any other suggestion is welcome.
I've done simple installs (.msi) with AI for some time but now have a project where the msi is run via GPO. And I'm not a network technician. So this installtion drops templates and a Word add-in (.dotm) in specific folders under Application Data (the AppData Roaming profile). As simple as that ...