As I was reading through the article, I was anxiously awaiting the appearance of the Schwartzian Transform.

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]

Quite a bit shorter than your code, and far less trickery and magic.

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