Even though you say that you “want to stick with Simple,” XML::LibXML (which is a binding for libxml2) will make your task far more “simple,” even trivial.   XPath expressions are the industry-standard way to look for things in an XML document, and they work beautifully in Perl.   Concerns for the exact structure of the document are removed from your Perl source-code and put into ... a string.   Support for anything you might want to do with an XML document is right here.

Furthermore, this library is the most widely-used tool (in any language) for both accessing and creating XML documents.   So, you are probably accessing the file with the same software that was used to create it.