What do you have in <...other lines that must be copied...> ?, and what is the attribute name in <label_y="somevalue">, that is not valid XML.
To remove the duplicate blocks, add a handler for the label_y tags to cut the element and then print at the end using an end_tag_handler.

my $label_y;
my $twig  = XML::Twig->new(
  twig_roots => { 
  'label_a' => \&label_a ,
  'label_y' => \&label_y ,
  }, 
  ,
  end_tag_handlers => { 
   'label_x' => \&label_x, 
  },
  twig_print_outside_roots => $OUT, # print rest
); 

sub label_y {
  my ($twig,$e) = @_;
  $label_y = $e->cut;
}

sub label_x {
  my ($twig,$e) = @_;
  my $y = $label_y->att('y');
  $label_y->set_att( channel => $y);
  $label_y->print;
}
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poj