Allow administrators to pick post author on custom post type edit screen

All users with author and contributor roles – actualy any in-built role above subscriber – should be available from the author dropdown. However, if you want organization_administrator users to be available also, you will need to assign those users a contibrutor or author role as well (anything more than subscriber.)

This seems to be due to a throwback from when WordPress had user levels instead of roles because the post author metabox is called with an argument of 'who' => 'authors'… It probably should not be this way any more but that’s how it is. See /wp-includes/class-wp-user-query.php where the who argument is checked:

 if ( isset( $qv['who'] ) && 'authors' == $qv['who'] && $blog_id ) {
        $who_query = array(
            'key' => $wpdb->get_blog_prefix( $blog_id ) . 'user_level',
            'value' => 0,
            'compare' => '!=',
        );

Alternatively, you can add 'level_1' => true, (or any level_* except level_0) to your role capability list, but you will need to remove and add the role from each user with it to trigger an update of the user_level user meta for that user. (Unfortunately there doesn’t seem to be an in-built way of updating this for all users of a role.)