hide out of stock items

No – sorry.

Would I be able to add a custom widget to my theme based on the category widget and change the code accordingly?

yes of course.

As there has not been an update to this topic for a while, I can only assume that the issue has now been resolved and I am now marking it as such. If this is incorrect, please feel free to change the topic’s status and/or post a follow-up.

Yes it was tricky to do. But finally got it to work.