I solved my problem by simply adding a checkbox so the user can decide if the object will be published or not. Perhaps not a perfect solution, but it did the job for me.

I've been able to get the versioned extension working on my DataObject! (sort of...)
$this->Fields() didn't work for me either, I was getting the same method error that someone else was getting, so I specified the DataObject I was trying to version - instead of $this->Fields, I used $this->HomepageResources() (substitute for your DataObject Class name)

So, the versioned table works if you add new entries, or if you change existing ones, HOWEVER, it does not update if I delete a entry.

Does anyone have any idea why this is happening or how to fix it?

Thanks