The reason for the collision seems to be because, by default, the context root, "/", is to be handled by org.apache.catalina.servlets.DefaultServlet. This servlet is intended to handle requests for static resources.
If you decide to bump it out of the way with your own servlet, with the intent of handling dynamic requests, that top-level servlet must also carry out any tasks accomplished by catalina's original "DefaultServlet" handler.
If you read through the tomcat docs, they make mention that True Apache (httpd) is better than Apache Tomcat for handling static content, since it is purpose built to do just that. My guess is because Tomcat by default uses org.apache.catalina.servlets.DefaultServlet to handle static requests. Since it's all wrapped up in a JVM, and Tomcat is intended to as a Servlet/JSP container, they probably didn't write that class as a super-optimized static content handler. It's there. It gets the job done. Good enough.
But that's the thing that handles static content and it lives at "/". So if you put anything else there, and that thing doesn't handle static requests, WHOOPS, there goes your static resources.
I've been searching high and low for the same answer and the answer I'm getting everywhere is "if you don't want it to do that, don't do that".
So long story short, your configuration is displacing the default static resource handler with something that isn't a static resource handler at all. You'll need to try a different configuration to get the results you're looking for (as will I).