Just an update. This problem has now been elevated past the senior technical support level to the engineering level at Apple. Engineers and managers there work on structural issues and compatibility between Microsoft and Apple.
The issue is this: When iTunes is installed on a Windows machine, there are actually about 4 separate programs installed on the Windows registry (Control Panel / Programs and Features). One of those programs has simply refused all attempts to install itself on my Windows 10 PC. It is the "Apple Mobile Support" program. The senior level technician spent approximately 4 hours total time (3 different sessions) on the phone including several remote support sessions where he was watching and coaching me through all sorts of program uninstall and reinstall, and specific driver installs. He even installed a specific program to force that one Apple program to install itself, and it also failed - twice. All attempts failed to get "Apple Mobile Support" installed.
Finally, he/we installed a WinRar program (??) used the command prompt to run and gather 6 different log reports from each Apple install component, compressed them, and sent them off to Apple. He has never seen anything quite like this before and elevated it to their engineering staff, as stated earlier. When his next shift is on (next week), or after engineering has responded, he will circle back to me with what is going on.
Praise: Even though this has, so far, been a very frustrating experience over a tiny electronic device, I am most impressed with the level of concern and expertise and persistence this guy (and Apple) has shown, in their effort to resolve this issue. Hats off to Apple support for their tenacity to keep even one customer happy. To have the very same senior support guy all the way through this process is exemplary! None of the old "repeating the same problem to 2 or 3 different people" frustration whatsoever. Support like this is quite rare - possibly unique - in my experience. Even though not fixed yet - huge KUDOS to Apple support.