VSphere Client not allowing export of OVF template

Well, this is embarrassing. Answering here so that someone else may find an answer, but I'm not proud of this one. :)

The solution was a simple one: Due to changing the port, neglected to also append the port to the login box in the vSphere Client.

So, updating from [machinename] to [machinename]:8443 worked just fine.

Thanks to RobM for starting me down the path of realizing I'd overlooked something basic.

It turns out that when we installed vCenter's SSO it automatically detected every Active Directory domain that it could. Many of our Departments run and manage their own Active Directory domains instead of using our central Enterprise Active Directory domain that we are using. This meant that we had half a dozen sizable Active Directory domains in the SSO's Identity Sources (Administration > Sign-On and Discovery > Configuration).

Removing the unnecessary Identity Sources resolved the issue.