This runs in 0.02s on my machine, compared with your original which runs in 0.3s. So 15x faster :-)

my($data, $n);
my $bufsize = 4096;
my $mask0 = "\xff\0" x ($bufsize / 2 + 1);
my $mask1 = "\0\xff" x ($bufsize / 2 + 1);

$data = "\0";
while (($n = read $file, $data, $bufsize, 1) != 0) {
    print $reversedFile 
        substr(((substr($data,2) & $mask0) | ($data & $mask1)), 0, $n)
+;
}
[download]

Dave.