Hi nickc,
Forgive me the long delay in providing a response but it took me a while to solve the problem. Since I don’t have advanced knowledge of Wordpress and you couldn’t help me with it, I contacted my hosting service (GoDaddy) and contracted their technical support specialists to do it. They upgraded the PHP, have all sites running on the latest PHP version (or one version before the latest) and the sites are running fine. After PHP was updated the problem remained as it was - the WP Migrate plugin still wouldn’t work. After working on the sites some more the specialist shared the problem was in the .htaccess file and he made some changes on it.
After these issues were resolved I was able to run the WP Migrate plugin, export all three Wordpress sites and import them into Local. The export process with WP Migrate and the subsequent import into Local couldn’t have been any easier. It worked exactly as you described and all three sites appear to be working just fine in Local.
I want to thank you one more time for you amazing support and for all the detailed instructions you shared so I could solve this problem.