I am sure you realize, something is still seen on your system causing the reinstall problem. It may even be some file which has a link inserted or some other components in common.
I think I remember seeing one thread where a substitute version of Excel needed to be installed which then allowed for the original version to be completely uninstalled. I cannot find that thread right now.
Have you looked in a Microsoft Excel forum?
You have gone to settings - Update and remove the option to download updates for more than just Windows? That might stop it from uninstalling long enough to find the problem.. You might also try uninstalling it in Safe Mode or running the uninstaller as Admin.