I'm not worried about replication, since I did a File -> Database -> New Copy (not replica, or OS copy) of everything (including search.nsf). So I know the search.nsf has a unique rep id. The search site configuration documents (2 of 3) definitely needed to be modified though, to reflect the correct new path. After I corrected the path, I deleted the search.ft directory and rebuildt the index.
And everything appears to be exactly what I was hoping for.