It's mildly ugly, but in fact it's not really slow or all that fattening :)

The only problem with it is that you're going to be carrying the Sort key after you no longer need it.

ST to the rescue!

sub computeSortKey {
   my $aref=shift;
   my $sort;
   my $M = 100;        
   for (@{$aref}) {
            $sort += $M * $_;
            $M = $M / 100;        
   }

   return $sort;
}

#Schwartzian Transform
@Tree = map  {$_->[0]}
        sort {$a->[1] <=> $b->[1]}
        map  {[ $_, computeSortKey($_->{Path})]}
        @Tree;
[download]

Note that I don't have perl on this PC, so I can't double check the code for syntax errors, but I think that'll work for you.

The advantages of doing it this way are that
1) it's a well known idiom, so a lot of perl programmers will grok right away what you're trying to do, and
2) you don't keep the sort key around after you no longer need it, so it keeps @Tree relatively clean.
--
Mike