Pardon me for jumping into an old discussion, but I have a comment on this, and a suggestion that, if coded, you probably would want to deploy universally in the theme. Standard practice for mobile layouts these days is to start by showing just a link/button with the word “Menu” and/or a menu icon (typically three horizontal lines), and when touched/clicked on, the whole menu (including sub-menu items) would open below it (and close when the Menu button is touched again). That would solve the problem James was having in February (which would indeed be a universal problem for anyone trying to access a site with submenus on a touchscreen device), as well as my concern, which is that the menu fills the whole screen on a small device, so every page change requires scrolling before any content can be seen.
Would you consider implementing this very common style of menu behavior?