This isn't an answer to your question, if I get time this week I'll have a look. I've not used Archive::Zip for this, however I do something similar at work and can confirm this method works to extract the xml to a variable:

use IO::Uncompress::Unzip qw(unzip $UnzipError);
#lots of unrelated code...

my $word = 'test.docx'; # In the actual script I was walking a NetApp 
+filer.
my $settingsXML;

unzip $word => \$settingsXML, Name => 'word/settings.xml'
      or die "unzip failed: $UnzipError\n";
[download]

I used this to detect various problematic settings in a vast archive of documents. IO::Uncompress::Unzip is a core module btw.