Sorry to hear you're not getting anywhere
You might want to reach out to support directly next. They might have some alternate suggestions, reinstalling from the system Administrator account etc. You can reach them via Contact Customer Care
Be sure to sign in with the Adobe ID associated with your membership to see the contact options
Dave, I called Adobe Support today as you suggested. I got through almost immediately. I was very impressed with that. Anyway, they tried an uninstall and a reinstall after stopping all Adobe related processes. I think the order in which the processes are stopped is important since none of them restarted. That was a problem I was having yesterday as you may remember.
Anyway, when we were done, I still had version 3.8.0.310 installed, not the newer 3.9.0.344 update. After some additional research the service rep found that the update had been pulled because of some issues. It would have save me a lot of concern had they flagged that on the download site.
Anyway, I will get a call and/or an email from the service rep when the update is again available just in case my installation of the Creative Cloud Desktop does not detect the re-availability. I'll let you know when that happens and if I can get the app successfully updated.
In the meantime, thanks for all your help yesterday!