It sounds like you guys may have had an issue with humidity loss which can happen from opening the lid too often and/or having improper hygrometer readings
This is what works for me/my experience... What usually happens is...
Day 14 of (coturnix) quail incubation, you raise your humidity from 45-50% to 65% and you stop turning them/take them out of the turner.
Day 16 to possibly 20 but mainly 17 should be hatching times if your temperature has been pretty stable at 100 degrees (for incubator with a fan) - keep in mind even the built in digital thermometers and hygrometers in incubators can be waaaaaay off! So you'll want to look into calibrating those for ideal hatch rates and chick survival. If those times were wonky or if some chicks have deformities then you may have had a temperature issue.
Even a drafty room/room that changes temperature night/day can effect development/hatch time.
So back to the point hehe - if your humidity is too low, the chicks will not be able to get out of the shell!
If your humidity is 65% but then you open the lid and let the humidity escape too long, *especially* if chicks have already pipped/cracked through the shell, the egg membrane will dry up (like shrink wrap you said?) trapping the fully formed, healthy baby in there to die and really you do not want to have to mess around further by rehydrating it (because you can't simply crack it out as the membrane has blood vessels connected to the chick and it can bleed out/get infection so best to help it rehydrate and let it come out itself) and further opening and closing the incubator, possibly disrupting other eggs and chilling chicks.
Hands off is the best approach I find
just keep the environment sterile and stable and let them do their thing and have someone help you take them out once a day - my roomie and I aced a system hehe - I hold the lid over a few inches (taking it off completely would be full humidity loss) and shine a light, attracting the chicks, she grabs a few, covers them and puts them in the brooder a few feet away as I whip out some cracked shells, then we repeat either the next day or if there are more than a handful ready, we wait about 15-30 minutes, the longer the better, obviously, then repeat it, probably without any shells but ASAP putting the lid back when the babies are out.
Sorry if this is way too much info as you guys have already hatched hehe
