Theme that includes a “core” plugin but the files in theme and child folder ignored

Unfortunately, that is not going to work.

Only files you find in the parent theme can be overridden in a child theme, and even at that it’s only the actual WordPress specific files that will be overridden.

The only real way you would be able to do this is if the theme developer integrated a function to check for those files, or used filters for it.

My experience with Qode though this is not possible at all, and you will not find any easy way of doing this.