I’m running everything on Windows 10, and everything is running as normal applications (no services involved), that is, all processes run under the current logged in user, who has full read/write access to all directories involved.
What is the (best) process for moving every single show, no matter where it is currently at, to one single UNC share/path?
Either stop Sonarr and move all series, then start Sonarr and update the series paths in the series editor. Or if you prefer to keep Sonarr running, select some series, move the files and update the paths then move more and update the paths. What you want to minimize is Sonarr rescanning a series folder when the root folder is not empty, if it’s missing and Sonarr sees the folder isn’t empty it will rescan and lose track of existing files (including unmonitoring episodes if Ignored Deleted Episodes is enabled.