I just tested on Composer 8.62 and I'm able to remove /private/tmp from the exclusions list without any issues. I exited/relaunched and confirmed the removal sticks.

Perhaps it's a corrupt preference file or something. Does anyone know how I can "reset" composer without removing existing packages?

It does sound like a corrupt preference to me. But before you delete anything, you should know that its not necessary to remove the /private/tmp path from the exclusions list. That really only applies to the snapshot process. If you open a Finder window to /private/tmp using Go to Folder or by opening it from Terminal. you can drag and drop anything in that directory into a Composer window and it will copy it in, allowing you to build a package with those files, regardless of the exclusions. For what you're trying to do with the Office install, that will work just fine.