I searched the platform for instances of AbstractCmsElementResolver and then mirrored the location in my plugin. So I added it to Plugin/src/Core/Content/Media/Cms/Type and used the namespace Plugin\Core\Content\Media\Cms\Type. I then added the service to my Plugin/src/Resources/config/services.xml.
I am not 100% about why this works, nor why I need to create a DataResolver, or if this applies only to when I copy an element, as when I created a new custom element I did not have to create a resolver. If anyone has an answer to this, that would be great