The Microsoft Uninstall/Install Repair Tool worked for me.
Now, I had a slightly different issue, which I think was prematurely deleted registry entries for Hamachi that were preventing proper installation via the built-in Windows installer. As a a result, I couldn't reinstall Hamachi, because the Windows registry entries apparently indicated that it was still installed.
The MS tool turned up two unnamed programs. Trying to fix the first one did me no good, but when I told it to fix the second one, that did the trick. For some reason, my Office 365 installation became corrupted, but reinstalling that fixed it right up.
So, thanks for the suggestion and I hope this info may help someone else.