Wouldn't it be easier just to use "tar" (the GNU version is the accepted standard, and it is available for all common platforms).

If a perl wrapper makes it more comfortable for you, here's a version of your script that is functionally equivalent(*) to the OP, but is a lot easier (and will run a lot faster, without using very much memory at all):

#!/usr/bin/perl -w

=head1 NAME

backup.pl - Yet Another Script for making backups

=head1 SYNOPSIS

backup.pl --bakdir=s --backup=s [--ignorefile=s]

Options:

    --bakdir     - where to look for and store backup files
    --backup     - what directory to backup
    --ignorefile - file which lists what subdirs not to backup

=cut

use strict;
use warnings;
use English;
use Getopt::Long;
use Pod::Usage;
use File::Path;

my $bakdir = '';
my $backup = '';
my $ignorefile = '';

GetOptions(
   'bakdir=s'     => \$bakdir,
   'backup=s'     => \$backup,
   'ignorefile=s' => \$ignorefile,
);

$bakdir ||= ".";
$backup ||= ".";
if ( $bakdir eq $backup ) {
   warn "We should not create a backup of $backup in $bakdir\n";
   pod2usage(1);
   exit;
}

eval {mkpath($bakdir)};
if ($@) {
   warn "Unable to find or create directory $bakdir\n$@\n";
   pod2usage(1);
   exit;
}

# create a tar.gz archive with a unique filename
my @t = reverse((localtime)[0..5]); $t[0]+=1900; $t[1]++;
my $t = sprintf("%4u-%02u-%02u-%02u-%02u-%02u",@t);
my $newbackup = "$bakdir/$t.tar.gz";

my @cmd = qw/tar cz/;
push @cmd, '-X', $ignorefile 
    if ( length( $ignorefile ) and -f $ignorefile and -r _ );
push @cmd, '-f', $newbackup, $backup;

exec @cmd;
[download]

(* footnote: it's not exactly equivalent -- I felt compelled to add a couple checks on the ARGV option values; more could still be done in this regard...)

For some reason, pod2usage did not work for me as expected, but with proper command-line args, this version does accomplish everything that the OP set out to do.

(updated code to add one more check on the "ignorefile" arg, and to remove the "debug" option, since it's not really needed here)