Because of the shadows/lighting, I can't get the right combo of lighting, contrast, color and saturation to make it show up better. Around 3 minutes in video, she stands up for the final time and I'm pretty sure the egg is visible at that time. She takes really deep pushes and then lifts between pushes. Some just stay low the entire time. I had posted here and on BCAW that she was in labor, but then deleted my post because I wasn't sure, especially since I couldn't see an egg and her pushing technique.
Anyway, it's here. Sorry I couldn't get the picture any better for you guys.
Here's Quest's labor video. I just uploaded it (3:10pm) and it is in the process of getting lightened so hopefully we can see the egg better once she lays it. But you can see her pushing and the final stand after last push to allow egg to dry