Hello,
Reading your task I am interested in the work to be done.
I am a Full-Stack Developer for four years, so I can both work with the Front-End as the Back-End. I focus on working with CMS like Presta, Magento and Wordpress. I can finish your task, had a simillar problem on a different site. The easiest solution is to call the PHP-function to create the subdirectory in the directory caller. I neither want to go further into detail, since this would make my work obsolete :) and I don't know exactly what menu theme you are using.
I am going to write you a full report on what to do at the end, but I also would like to offer you to create a child theme, that when you update your theme, any changes done to the code no longer is overwritten.
If you have any questions, feel free to get in touch.
Best Regards
Frederik Fleischmann