I discovered that the URL string needs to point at the public php.
final String URL = "http://www.naturallyIrrational.com/naturallyIrrationalsoapserver.php";
Really a very simple thing in the end after 3 weeks. Downloading the source code was essential as it allowed me to see the service is functioning. There was/is another issue regarding passing parameters, like this:
PropertyInfo pi = new PropertyInfo(); pi.setName("valname"); pi.setValue("rt2"); pi.setType(String.class);
but that is a different question.
Thank you for your comments.