Include sticky posts on the static page front page

I’m guessing that in get_option( 'sticky_posts' ) is array of posts that are sticked? I suggest changing this method to post meta values.

You could mark news as sticky by adding post meta to news, for example
add_post_meta($post_id, 'sticky_post', 1);
and then you should order posts by this meta:

$args = array(
    'post_type' => 'news',
    'meta_query' => array(
        'relation' => 'OR',
        array( // get posts with sticky_key value = 1
            'key' => 'sticky_post',
            'value' => '1', 
        ),
        array( // get posts with sticky_key value != 1, so this is rest of posts
            'key' => 'sticky_post',
            'value' => '1',
            'compare' => '!='
        )
    ),
    'orderby' => array(
        'meta_value_num' => 'DESC', // first order by sticky_post value, so you could create levels of "stickness"
        'post_date' => 'DESC'       // then normal sort
    )
);

$query = new WP_Query($args);