Would it be possible to have in the documentation how that demo page was built out?
The demo page looks GREAT!! and it has organization between multiple categories as well as sub-categories, but thread after thread people have a hard time building that functionality. It would be helpful to see what was done in the staged site. I’ve tried overriding themes and the code isn’t that intuitive.
The Restaurant Menu plugin Demo was built on the base of our free Oceanica Lite theme, so I would recommend that you download and install the theme to check out its structure. Perhaps, it would be much easier for you, if you build staging website based on the theme first.