Mike
here is a
listing of all Fastmail domains.
AFAIK, by clicking on secure Login you automatically use the Fastmail SSL certificate. This is done automatically via a redirect to Fastmail.fm. I believe it is simply too expensive for Fastmail to purchase certificates for each and every domain they own, thus they use the redirect method.
It is a pity that your work's net nanny seem to automatically associate the other Fastmail owned domains to Fastmail.fm in the way you describe.
By the way all Fastmail's domains point to the same servers (in NYC), the problem you are getting is the association via the SSL certificate. As far as I understand it.
Ed