I did follow the orthodox procedure - it is pretty standard for this situation. First use Control Panel to uninstall, then use the removal tool. Every time I tried to uninstall via Control Panel - whether I went to the Control Panel via the Classic Shell (which still works in Windows 10) or by the route listed by McAfee (which gives you a different looking screen, more "iconized") it would say "Navigation to the Web site was cancelled" or words to that effect. That was what stymied me. The McAfee instructions do say if Control Panel fails, go ahead and run the Removal Tool (when you go to do that, it says "Be sure you have uninstalled via Control Panel before running the Removal Tool" or words to that effect). So finally I did run the Removal Tool and it did, so far as I can tell, remove all the remaining McAfee components. I thereupon installed the Avast software instead. Now I just have left juggling multiple Avast licenses (2 computers and one smartphone). I expect Avast will help me with that if necessary.
So I guess this issue is solved. I would, however, for the sake of peace of mind, like to know if there is an easy way to check that all bits of McAfee have really been removed? File names or registry keys to scan for?
Just a footnote - this is the fourth Dell machine (two mine, two at the office) on which I have removed McAfee, and the first time the uninstall from Control Panel did not work. I've also done antivirus software switches on a number of other machines belonging to others, and never had a problem before.