Have you thought of going down the route of adding some custom CSS?
Looking at Babel, it seems the class elements in question are .x-menu-list and .x-menu-list-item. Create an additional @media query for your mobile devices for these elements. You could either just display the fly out menu as default with no hover or change the :hover to pointer-event so the fly out appears on touching the screen.
I've not investigated the CSS so you'd need to a bit of digging to see exactly what style was applied to which element.
