My goal is to have port 80 and 81 listen and serve content from two distinct paths. I\'m looking at replicating what I used to do with IIS and creating websites on specific
I think you're on the right track, but you're just missing some of the child elements that are listed in the specification for the Service element.
I think you're just forgetting the Engine and Host elements, which are grandparent and parent respectively to the Context element.
For more information and a more detailed example, which defines two Service elements, one on port 8080 and one on port 9080, see this mailing list post:
http://www.mail-archive.com/users@tomcat.apache.org/msg44729.html