But alas, even though you mention it in the title, and once in the body, you never got to it. Just the GRT, and Tye's particular trick.

I still think that the ST is always clearer than the GRT, and that jumping to the GRT without careful consideration is a case of premature optimization—except for those rare cases where the work required to wiggle your data into a single sortable string isn't all that unobvious.

By contrast, here's "sort a list of IP addresses" using the ST:

my @sorted =
  map $_->[0],
  sort {
    $a->[1] <=> $b->[1] or
    $a->[2] <=> $b->[2] or
    $a->[3] <=> $b->[3] or
    $a->[4] <=> $b->[4]
  }
  map [$_, split /\./], @inputs;
[download]

So, it's too bad your title is a letdown. Good analysis, otherwise.