Sorry to keep you up and waiting for news, CluckNDoodle, but it was too late after I finished to check in.
(You might notice that I say "she" and "her" when I am talking about Valor. We actually have no idea of her gender, but we decided to hope for the best and therefore guessed she was female.)
As it turned out Valor was more tired than we thought. Piece by piece, we took of the whole top half (the air packet half) of the shell, membrane and all (didn't see a single blood vein in the membrane). Once again, thanks for the coconut oil tip,
@LilyD, it made all the difference. The membrane near the zip was so dry that it was like a second layer of shell, and Valor was so dry that we put coconut oil on all exposed places to give she some moisture.
After the top was off Valor was still wiggling so we thought she would make it out by herself. We added a wet rag and a cup of water and, of course, Valor in his bottom shell. For five minutes we say on our hands while we watched before deciding he just needed a bit of time. We forced ourselves to leave the room.
10 minutes later (we had set a timer and everything) we were back. No progress. We took Valor out and angled the egg so it was angled down, helping her out. We chipped off a bit more of the shell and added more coconut oil and Valor "hatched"!
But there was one problem, her head appeared to be stuck under her wing. My helper panicked, saying "I can't do this!" This was probably the scariest part of the whole process. I comforted my helper, and we continues. With cue-tips I held the wing back and tried to push up the head so my helper could slide the cue-tip covered in coconut oil under, but the head was stuck. At this point I panicked and said stuff like, "she's not going to make it! She has a birth deformation that makes her head stick to her chest! We can't help her, we should 'put her down'!" My helper comforted me and said "it's just the membrane. This is a healthy chick, she is going to be okay." We tried again, and my helper was right, the membrane was sticking the head to the chest. With the help of the coconut oil we freed her head, but she still kept it curled down under her wing.
We put her in the incubator and left her for the night. I was literally shaking with relief that we didn't kill the chick. We watched a movie to calm our fears about the poor chick downstairs. By the time we finished it was 12:30 at night.
The next day I checked on Valor. Because she had been in the egg for so long I guessed that she was running out of the yolk in her stomach and I had it in my mind that if she was strong enough I would give her food and water. But now that she was half-dry I saw that my fears had been confirmed. The chick was too skinny and it's legs and neck were not thick enough to ever support any weight. The beak was too large for her head. I realized that Valor would never survive. We culled her this morning. I don't know what method was used because it wasn't me who did it.
Yes, I am sad. But I think it was better this way, because I wouldn't want Valor to live her whole life in pain.
Even if the assisted hatching didn't work I'm glad I got the experience. I know now that I should have acted sooner, so I will remember that for next time. Thank you everyone who helped make it possible for Valor to be able to stretch outside of the egg and enjoy freedom, if only for a few hours.