Hi Zac - there is an enhancement request in the Product Plan to make it easier to do this.
It's ENH-000112313 - User would like a functionality to change the default home folder location of ArcGIS Pro by modifying the registry settings.
User would like to have a functionality by which they can change the default home folder location for multiple users at same time and not changing it within the settings by launching ArcGIS Pro individually. By default the folder would be created on user’s C: drive but, user wants the folder to get created on user’s network drive as it will help them to manage the storage space. And....
And ENH-000113891 - Provide a mechanism for GIS administrators to deploy user.config settings to their users