Hi Matt. Instead of futzing with registry group policy (which can have all kinds of nasty side effects, and may be rolled back by changes in group policy upstream of you) I suggest using scripts that use Windows environment variables to modify the seat type and license manager. I think this is easy workaround that doesn't require any tricky Windows permission setups. I have posted an example script here.
ArcMap Basic Standard Professional Startup Script
Another approach which I think is better (less risky) than wholesale registry permissions changes is to use a securely accessed script that is set up in Windows to crank up as elevated to do a specific task like this (modify registry keys to change seat licensing) that users can launch from Windows Software Center.
Hope this helps!