Whats the answer?
I decided to go with Basic Authentication. You cannot use the proxy mechanism since you don;t have a logged in user.
Enable Basic Authentication on Server
You will need to rebuild your CAS overlay war. Add the following dependency to your pom.xml file.
Java Utility Class
This class sets up a Apache Http Client. It is also used to set the headers on the request. I found that preemptively sending the Basic Authentication headers was the way to get it to work.