I found a video , that shows how to replace the keyboard. In the process you can see the tech removing the screen assembly and disconnecting it from the board. It's not the best video, but in the beginning they remove the screen connectors and then the assembly around 5:35 https://www.youtube.com/watch?v=8Amsg6VgD9w
Edit: here's a video of of a 9550, https://www.youtube.com/watch?v=knVC-iiCm-w
not sure how similar it is to the 9570, but I'm going to try this in the next day or two, I currently have two 9570s' and I'm going to swap the screens on them.