Thanks for your comments.  Like Nijdam and Rick, I am familiar with the Paper by Morgan et al and I fully understand its conclusions, which are what you state in your conditional answer to the problem.  Where I disagree with Rick and Nijdam is that I believe that, although not actually wrong, the Morgan paper is seriously flawed in many ways resulting in its being next to useless as a basis for an explanation of the Monty Hall problem.  I am very happy to discuss this if you have time.