How about direct sql with a simple subquery to first get all the post ids of your custom post type ex:
function get_all_comments_of_post_type($post_type){
global $wpdb;
$cc = $wpdb->get_var("SELECT COUNT(comment_ID)
FROM $wpdb->comments
WHERE comment_post_ID in (
SELECT ID
FROM $wpdb->posts
WHERE post_type="$post_type"
AND post_status="publish")
AND comment_approved = '1'
");
return $cc;
}
Usage:
$total_comments = get_all_comments_of_post_type('some_post_type');