Hi John, thanks for your reply and for your code!
After all, I think this is what I did (hard code the post_type), except for removing the 'post__not_in' => array($post_id),
just because my form can both edit and create a post.
So I wasn’t that wrong, was I?
Actually, it worked that way but I’m afraid that it could have a flaw and I am not seeing it.