How do I improve this admin query snippet to avoid generating duplicate results on non-meta searches?

A GROUP BY statement can group your posts after the JOIN. For WordPress you can use the posts_groupby filter.

add_filter( 'posts_groupby', 'my_post_limits' );
function my_post_limits($groupby) {
    global $pagenow, $wpdb;
    if ( is_admin() && $pagenow == 'edit.php' && $_GET['post_type']=='listings' && $_GET['s'] != '' ) {
        $groupby = "$wpdb->posts.ID";
    }
    return $groupby;
}