How to update Windows DNS server with Linux DHCP client hostname?

[Patrick Doyle]

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;