Update: I was able to get it "working" by doing the following two things.
Copied JBOSS_HOME>/server/default/deploy/jbossweb-tomcat50.sar/web.xml to <JBOSS_HOME>/server/<config-name>/conf/web.xml
And added a Context entry to jbossweb-tomcat50.sar/server.xml
I would like to be able to do this within the META-INF\context.xml from the war itself to provide as much mobility as possible for the servlet. Simply moving the context from server.xml to context.xml doesn't work. Instead it redirects all requests to that app to the external directory.
As of now, I am wondering if this is a bug in tomcat and not a configuration error. The Host and Context handling in both tomcat and jboss-tomcat are a huge mess.