I think I managed to find a smoking gun or at least close enough to it to find a solution.
My system would not start TrustedInstaller (Windows Modules Installer) apparently due do some sort of an error in the registry. When WSUS returned some of its errors and Aker pointed out that the Update Agent was old - I tried to manually install an update agent with WindowsUpdateAgent-7.6-x64 but it returned an unrecoverable error trying to do the update.
Another clue was that SFC/ scannow would not run because it could not start the repair service. After some looking around, I found that this was likely because Windows Module Installer would not start, returned error 1067, and terminated. I used a utility from
http://www.tweaking.com/content/page/windows_repair_all_in_one.html to help repair the registry entries related to the Windows Module Installer. I had just done a fresh image of the system, so I was not too worried about this tool which is very heavy handed. The repairs were done in Safe Mode, and when the PC booted back up, Windows Modules Installer was working fine. I then updated the Windows Update Agent successfully and also manually installed KB3135445, both of them would not install before. I rebooted and now the normal Windows Update is working normal. It quickly found 149 updates, downloaded them and is installing them right now.
The utility from Tweaking.com is not a 'registry cleaner' it is a troubleshooter that spends a lot of time and effort fixing issues in the registry. It does allow the user to control how heavy it gets applied and provides resources to backup the registry and create a restore point if things go bad. I personally had a fresh offline image made to my NAS since I had no idea if this was going to fix anything or permanently obliterate my machine. Turns out that it worked and things are looking up. This machine has gone through the ringer and I can hardly believe it is nearly back to tip top shape with all my special licenses, settings, and configurations intact. The crash and subsequent restore failure was quite a challenge. The registry hives in particular were corrupted when the machine was imaged.
Very thankful for the help of this utility and the support of the forum.