Ok. It finally took a complete uninstall/reinstall of Active Perl to fix whatever was up with my system.
Here's the 'finished' product - for posterity.

use HTTP::Daemon::SSL;
use HTTP::Status;

use SOAP::Lite;
use SOAP::Transport::HTTP;

# my soap package
use auth;

  # Make sure you have a certs/ directory with "server-cert.pem"
  # and "server-key.pem" in it before running this!
  my $daemon = HTTP::Daemon::SSL->new(LocalPort => 8001)
         || die;

    my $soap = SOAP::Transport::HTTP::Server
        -> new ( )
        -> dispatch_to(qw(auth));


  print "Please contact me at: <URL:", $daemon->url, ">\n";
  while (my $conn = $daemon->accept()) 
    {
      while (my $request = $conn->get_request()) 
      {
            $soap->request($request);
             $soap->handle();
            my $response = $soap->response();
            $conn->send_response($response);
      }
      $conn->close;
      undef($conn);
  }
[download]

This will 'service' my soap requests at https://<server>:8001.

Thank you very much for your extensive help on this matter. I wouldn't have gotten anywhere without it.