I believe the "turn of the screw" in fact refers to an old torture apparatus, where each turn of the screw amplified the pain of the subject. Here are a couple of examples from literature where this meaning seems clear:
1. "Just when it seemed to him that another turn of the screw would kill him, little Stanislovas stopped." from The Jungle by Upton Sinclair
2. "He perceived himself so extremely forlorn and lamentable, and was moved so deeply by the oppressive sorrow, that another turn of the screw, he felt, would bring tears out of his eyes." from Tales of Unrest by Joseph Conrad
I hope that helps, Annie.
