Hi Al,
Somewhat off-topic, but as a professional sysadmin of many years I've got to respectfully disagree with your statement that the "security perspective for LibreOffice is no different than it is for any other software on your server".
Installing a desktop application on a Linux server can open you up to all kinds of interesting vulnerabilities that may or may not be addressed by future security updates, patches, etc. Even though unoconv runs LibreOffice in headless mode, LibreOffice is still dependent on many X-Windows tools and libraries. Those dependencies are installed automatically when you install the LibreOffice package.
As X-Windows is a network-enabled desktop environment by design, you should be careful when installing it on a production, internet-facing server. An admin unfamiliar with X-Windows configuration could inadvertently open themselves up to attacks that rely on standard X-Windows features, not bugs or vulnerabilities that would be addressed by future security updates.
That's not to say that unoconv & LibreOffice are a bad idea on a production server, but it does make things more interesting from a security point of view and is not the same as installing a new web server or other server daemon.