After creating a copy of the door frame low, and adding a displacement modifier and a subdivision surface, you added creases to nearly all edges. This includes all the edges added previously when triangulating.
Rather than adding creases to nearly all the edges, would it perhaps work better if you first Select Sharp Edges, and then only add the crease to those?
I tried this, and I needed to add a couple of extra creases in lines leading to concave corners, but overall it seemed to work ok. Just wondering if I am missing something.
