How to force iCloud logout on Macbook Pro; Apple ID was deleted

I was on the phone today with an Apple advisor dealing with unauthorized charges on my Apple account and I ended up creating a new one and having the advisor delete the old Apple ID. It's gone for good. There's no way to log into anything or retrieve it. It no longer exists. Then I realized that in everything else, I had forgotten to log my Macbook Pro out of iCloud. Now I'm trapped in the nonexistent Apple ID, because it wants the password, but the ID no longer exists.

How do I force my computer to log out of iCloud? The Apple ID is 100% irretrievable so that is not an option. I've already tried turning my internet connection off and logging out that way. It didn't work.