Alright, so this took some fiddling with ProcMon, but I think I have an answer. You'll need to test it, though.
ProcMon got me to this part of the Windows Registry:
And you can see the "File" key has the path. Since it's in the registry, should be easy enough to set a GPO to set that on machines or use PowerShell to adjust it. I went and played in my lab domain for a bit and came up with this, which I believe makes all the required changes (see attached).