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I never imagined this would be as easy as it was. In my case I'm using a specific mobile theme and a switcher plugin. Four simple steps:
1. Upload dropdown-menus.php file in /dropdown/ folder of Mobile theme
2. Add code to mobile theme's function.php to 'include' the plugin (not sure if this is necessary):

if ( ! function_exists( 'dropdown_menu' ) )
    include( 'dropdown/dropdown-menus.php' );

3. Add dropdown_menu function call code to header.php, e.g. below logo, see plugin description. Something like:

$ddargs = array(
		'dropdown_title' => '[Main Menu]', // text to show when on page not in menu
		'indent_string' => '- ',	// text to show before 'indented' sub-menu item, repeated
		'indent_after' => ''		// text to show for sub-menu, NOT repeated
		);
dropdown_menu( $ddargs );

4. Style CSS: e.g. Add css to Mobile theme's style.css

.menu-top-menu-container {
	padding:5px;
	background-color: #e2e2e2;
}

Thanks!