I think you answered your own question (Effectively deal with the global hash variable (by redefining it?)). Can't you just let the last thing on @stories be the hash reference and not even deal with the hash?

sub StartTag {
      # Other stuff okay... but add..
      if ($tag eq 'story') {
           push @stories, {};
      }

}
# This subroutine is mostly superflous now I think...
sub EndTag {
  pop @curr;
}
sub Text {
    unless ($curr[-1] eq 'story') {
        $stories[-1]->{$curr[-1]} = $_;        
    }
}
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And that might do it. (untested)