You'll need to perform the stat calls before the sorting.

@a =
   map $_->[0],
      sort { $b->[1] <=> $a->[1] }
         grep defined($_->[1]),
            map [ $_, -M $_ ],
               @a;
[download]

You might even get a speed boost from the reduced number of stat calls!

[Oops, this is basically identical to tybalt89's post, but it hadn't been posted yet when I started composing this post.]