Using a custom sort routine, you can redefine the sort behavior for a specific condition. Here's an example of something that always puts empty strings last, but otherwise sorts alphabetically:

sub by_blanklast
{
     if (!length($a->[0]) ^ !length($b->[0]))
     {
          return length($b->[0]) - length($a->[0]);
     }

     return $a->[0] cmp $b->[0];
}
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You can use this in your code like this:

 } sort by_blanklast map {

In my testing, this seems to work like you want.