Please take a look at the Aperitive theme from Themes Kingdom, specifically the Menus page: [url removed, login to view]
Menus are a custom post type in the theme and it allows me to set a featured image, and I would like the featured image to show up in the menu like the screenshots I have attached. Those are quick mockups that I have done in Photoshop.
Would like this to be in a child theme so I can update in the future. If not, I would like to have a detailed description of code changes you have made.
I can send you the theme and documentation so you can take a look at it before proceeding.