I'm nowhere closer (as far as I can tell), but I've just enabled syslog to dump everything and I've noticed that when dhclient starts up, after it gets its IP address, it logs the following message: Unable to add forward map from <hostname> to <A.B.C.D>: timed out where <hostname> is the name I specified in the dhclient-eth0.conf (I've tried just the hostname, and the fully qualified hostname, with and with out the trailing period) and <A.B.C.D> is the IP address fetched from the DHCP server.
From everything I've read, I believe that I should be able to enable
this by adding the following lines to /etc/dhclient-eth0.conf: send fqdn.fqdn "<hostname>"; send fqdn.encoded off; # or, perhaps "on" send fqdn.server-update false; and I've tried send fqdn.no-client-update off;