Uninstall all adobe products silently

I'm trying to remove all Adobe software silently on our campus windows machines.  I can acheive this with the creative cloud cleaner tool with one problem, it does not remove start menu shortcuts.  Most of our end users don't have admin credentials, which are required to delete these shortcuts.  It's difficult to delete these with a script since we do not know which products and what versions of those products the user has installed.

Does anyone else have a good method to completely remove adobe products silently?