Did you look at my previous suggestion regarding the "g" regex modifier? Here's how to use it:

#!/usr/bin/env perl 
use strict;
use warnings;

open (my $original, '<', 'data.txt') or die $!;
open (my $fh, '>', 'output.txt') or die $!;

my $first = <$original>;
print $fh $first;
my @replace = $first =~ /"([^"]*)"/g;

while (my $line = <$original>) {
    $line =~ s/(\d{2})/$replace[$1]/g;
    print $fh $line;
}

close $original;
close $fh;
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Is that concise enough for you?