return $string . reverse $string;
[download]

That only generates even length palindromes. I instead suggest

return (
    $string
    . ( rand < .5 ? $letters[ rand @letters ] : '' )
    . reverse $string
);
[download]

Also, Don't Repeat Yourself. That's far too much copy-paste code there. Look at the benchmark script I wrote: much less code, and it tells you exactly which input strings each solution failed on and what it produced instead.