Where should I copy a PHP file from wp-includes to, in order to override it in my child theme?

You don’t need to change the core file. They’re classes which means they can be extended. It’ll require a bit of leg work but all you need to do is load an instance of the class and then extend/add to it. That’s the beauty of OOP.That’s if there isn’t a hook to modify things with already, which there probably will be.