Disk management on the afflicted laptop shows only the expected stuffs: two partitions on the internal SSD, an external HDD and the unlettered "For internal use only" gubbins that Microsith puts on there.
Registry shows entries for drive letters C through to H, which is more or less expected, plus one for P. Which isn't. Z absent.
To further plicken the thot, if I reboot with the box attempting to mount Z, then trying to access ElGordo from the "Network" bit in the left pane of Windows Exploder also doesn't work, though it does helpfully offer to run network diagnostics. Which, natch, do nothing. Reboot sans Z and ElGordo’s contents may be accessed from there as expected. Setting up a Network Location pointing to \\ElGordo\Public does similar: "\\ElGordo\Public is not accessible. Contact ur administrator. Stop messing with things Man Was Not Meant To Know. Srsly. Put the mouse down and step away."
Mapping two drive letters to the same location is untidy but on the whole the "map V and Z" thing seems simplest as it won't require rejibbling umpteen batch files spread across three boxes. A longer-term option is to pension off ElGordo altogether and replacing him with something newer, bigger and faster. He's so amazingly primitive that AFAICT he doesn't even do gigabit ethernet and the last firmware update put out by Seagate was about five years ago. PC World are knocking out a 4TB WD box for a hundred and fifty notes at the moment...