This may be completely off-base (and might not work precisely on odd numbered lists) but is an in-place transform within the scope of the solution? Seems like it might be quite fast, especially if you only need to transform some lines and do that with random skips through the original.

use warnings;
use strict;
use IO::File;

my ( $sum_orig, $sum_new, $lines, $lines_new );
open my $out, ">", "reorganized.txt" or die $!;

while (<DATA>)
{
    my ( $size, $file ) = split;
    $sum_orig += $size;
    if ( defined ( $_ = <DATA> ) )
    {
        my ( $size2, $file2 ) = split;
        $sum_orig += $size2;

        my $max = $size > $size2 ? $size2 : $size;
        my $rejigger = int rand($max/2);

        my $tmp2 = $size - $rejigger;
        my $tmp1 = $size2 + $rejigger;
        $out->printf("%-7d %s\n", $tmp1, $file);
        $out->printf("%-7d %s\n", $tmp2, $file2);
        $sum_new += $tmp1 + $tmp2;
        $lines_new += 2;
        $lines++;
    }
    $lines++;
}

print "Original average: ", $sum_orig / $lines, $/;
print "     New average: ", $sum_new / $lines_new, $/;

__DATA__
4329   file1
12311  file2
657    file3
4271   file4
20     file5
10001  file6
[download]