I completely agree that the injuries are caused by pulling out of the egg, but I think that's true whether you pull them or they try to pull away too soon. Over the summer, I had a number of chicks try to hatch too early by themselves, with bad injuries. They had no more assistance from me than the fact I was standing over the incubator whistling to them. I had them on their sides in the incubator. I'm going to try to never do that again. This last time I hatched in the carton. When they could zip by themselves (see above about the humidity problems) They would rest, leaning over the top of the egg for about 12 hours. When I had to help the shrink wrapped chicks (the procedure took me about 6 hours, btw--that's what I meant by go slowly), once I had the egg chipped off and the membrane removed, about 12 hours later, the chick would pull himself up and out, about the same as if he'd done everything himself.
I did lose a few chicks by giving them the 24 hours or so after I noticed the pip so I shortened the time somewhat. In my case, none had yolk that wasn't absorbed. Of the ones that died after I helped, one was zipped completely but unable to push the top off the egg. He lived for a little white after I discovered this and helped him out. The other may have gotten cold one evening when I was giving a couple of chicks away.
I did lose a few chicks by giving them the 24 hours or so after I noticed the pip so I shortened the time somewhat. In my case, none had yolk that wasn't absorbed. Of the ones that died after I helped, one was zipped completely but unable to push the top off the egg. He lived for a little white after I discovered this and helped him out. The other may have gotten cold one evening when I was giving a couple of chicks away.