As for overriding, I think one of the best options would be to have options in the menu items themselves as to select a different article or whatever the menu item type is for the mobile devices. For instance, the current setup for the menu is to create your menu item, select it's item type (lets say single article), and then select the article you want.
A great way to solve this problem of having different content for the mobile browsers is to have two different select boxes for the articles. One article would be for the desktop and one would be for the mobile browser. Developers could do this in their menu items as well by serving up different menu item types for their component. Just for example using the single article menu type, you could have another menu type that's called "Desktop and Mobile Single Article" or something like that where you can specify two different articles. Here is an image of what I'm talking about:
Most of the time just using media queries and styling with CSS will work but pages that are specifically styled for the desktop would have to have a separate way like this to serve different content for the smaller screen.