I wanted to do two things - read a section at a time, and write the output file from back to front. This allows a single pass through the input file.
Since the sections don't have an obvious ending, reading into the next section is required, but that's easy to fix when it happens :)

#!/usr/bin/perl

# https://perlmonks.org/?node_id=1216436

use strict;
use warnings;

my $inputfile = 'd.1216436.in';
my $outputfile = 'd.1216436.out';

my $pointer = -s $inputfile;           # output will be same size as i
+nput
open my $in, '<', $inputfile or die "$! opening $inputfile";
open my $out, '>', $outputfile or die "$! opening $outputfile";

local $/ = "\nTitle";                  # too far, but we will fix it
while( <$in> )                         # read whole section
  {
  s/\n\KTitle\z// and seek $in, -5, 1; # if read too far, fix & backup
  seek $out, $pointer -= length, 0;    # backup output pointer
  print $out $_;                       # put in proper place
  }

close $out;
[download]

Now if I can only stop giggling :)