I understand.
The copy script is simply copying the wrong element there, and this method may actually make a worse score, as printing the search bar twice.
Once the search element is moved, the plugin has to try to detect and re-initialize it, and that unneccessary extra work. Moving 3rd DOM nodes via javascript is a very bad practice, as it detaches event listeners from the origin element as well.
If you decide to keep this method, I would advise to move the search into a container element of your own, and move that element instead. That will keep your code functional, even if we make a minor change to the search output.
Your method was probably working for an earlier version of the plugin.