My first attempt at reassembly had the hinge making a terrible snapping sound due to pushing some plastic parts out of the way at full extension. After screwing in these first two screws, I suggest opening and closing the hinge a few times to confirm it's smooth and quiet. If not, you have a fraction of a millimeter of play to get it into just the right position.

Reassembly: I had difficulty going straight down. The connector has some angled edges that made it difficult. Instead, I slotted the wire side in first, then rocked it forward towards the hinge into position.