How do I access the menus produced by Dashboard > Appearance > Menus

First: Use, for options(), the Settings API (tutorial).

Second: Take a look at the core function and the available filters. Then take a look at the available filters:

$sorted_menu_items = apply_filters( 'wp_nav_menu_objects', $sorted_menu_items, $args );
$items = apply_filters( 'wp_nav_menu_items', $items, $args );
$items = apply_filters( "wp_nav_menu_{$menu->slug}_items", $items, $args );