Charset issue in Control Panel
I'm going to attempt to answer my own question now that I have had the issue resolved. Clearly this is a local server environmental issue. The explanation I have received from the hosting provider is not one I understand too well, but here it is for the record.


  For security reasons, the PHP FPM process on your server executes
  scripts in a separate chroot(2) environment, meaning that only a
  limited set of resources are available at runtime.  This sometimes
  causes problems when the chrooted program requires resources that
  don't exist outside the chroot environment that are loaded during
  runtime rather than being built in to the binary, or dynamically
  linked before the system chroot call.  The iconv extension has this
  problem, in loading .so binary data files corresponding to the
  encodings it's manipulating.  On your server, the files it loads were
  in /usr/lib/x86_64-linux-gnu/gconv, and had not been copied into the
  chroot environment at /srv/php-fpm/rdc.  Copying the contents of
  /usr/lib/x86_64-linux-gnu/gconv to
  /srv/php-fpm/rdc/usr/lib/x86_64-linux-gnu/gconv has fixed the issue.