Wordpress - How do you use a CPT as the default home page?

Thanks to @toscho for the useful answer, but it felt a bit hackish to me, so I poked around a bit and figured out I could add a filter instead:

function wpa18013_add_pages_to_dropdown( $pages, $r ){
    if('page_on_front' == $r['name']){
        $args = array(
            'post_type' => 'stack'
        );
        $stacks = get_posts($args);
        $pages = array_merge($pages, $stacks);
    }

    return $pages;
}
add_filter( 'get_pages', 'wpa18013_add_pages_to_dropdown', 10, 2 );

---

Update

After adding the above code I was, indeed, able to use a custom post type as the home page, but WordPress would redirect the permalinks because it wasn't a "page" post type. So http://localhost/test would redirect to http://localhost/test/stacks/home-stack, which wasn't what I wanted.

Adding this action, though, fixed that and queries my custom post type along with pages for the home page:

function enable_front_page_stacks( $query ){
    if('' == $query->query_vars['post_type'] && 0 != $query->query_vars['page_id'])
        $query->query_vars['post_type'] = array( 'page', 'stack' );
}
add_action( 'pre_get_posts', 'enable_front_page_stacks' );

Maybe so? Refined version of my earlier solution.

add_filter( 'wp_dropdown_pages', 'add_cpt_to_front_page_dropdown', 10, 1 );


/**
 * Adds CPTs to the list of available pages for a static front page.
 *
 * @param  string $select Existing select list.
 * @return string
 */
function add_cpt_to_front_page_dropdown( $select )
{
    if ( FALSE === strpos( $select, '<select name="page_on_front"' ) )
    {
        return $select;
    }

    $cpt_posts = get_posts(
        array(
            'post_type'      => 'YOUR_POST_TYPE'
        ,   'nopaging'       => TRUE
        ,   'numberposts'    => -1
        ,   'order'          => 'ASC'
        ,   'orderby'        => 'title'
        ,   'posts_per_page' => -1
        )
    );

    if ( ! $cpt_posts ) // no posts found.
    {
        return $select;
    }

    $current = get_option( 'page_on_front', 0 );

    $options = walk_page_dropdown_tree(
        $cpt_posts
    ,   0
    ,    array(
            'depth'                 => 0
         ,  'child_of'              => 0
         ,  'selected'              => $current
         ,  'echo'                  => 0
         ,  'name'                  => 'page_on_front'
         ,  'id'                    => ''
         ,  'show_option_none'      => ''
         ,  'show_option_no_change' => ''
         ,  'option_none_value'     => ''
        )
    );

    return str_replace( '</select>', $options . '</select>', $select );
}

Why not just create a front-page.php template file, that uses either a normal query/Loop, or (if a custom Theme option is set to display the CPT on the Front Page), outputs a custom query/Loop, based on the CPT?

The issue there is that you would have to create a separate Theme option to control the Front Page output, while at the same time instructing users to set Front Page to static page.

To make things easier, you could hook your Theme option into settings-reading, using the "Reading" option group in your call to register_setting via the Settings API, so that it displays with the existing Front-Page options.