When reassembling, I tied a piece of thread to the eyelet, wrapped it round the three antenna wires, and pulled it through the gap from the other side. It was still a tight squeeze though.
"Fully open the screen" is important - I left mine at 90 degrees and after removing the screws, the hinges wouldn't slide out of the main body. I had to open the hinges more to get the two halves to separate.