There are several things that could cause that. You might look through this link and see if you see something that jumps out at you. You looked at them. I didn't.
Mississippi State Incubation Troubleshooting
http://www.poultry.msstate.edu/extension/pdf/troubleshooting_incubation.pdf
Opening eggs is hardly ever a good thing to do. Before a chick hatches it has to position itself, dry up blood vessels outside its body it no longer needs and absorb the blood, absorb the yolk, do something with that stickly stuff outside its body so it dries fluffy instead of all glued down, learn to breathe in air instead of living in a liquid environment, and who knows what else. Some chicks do a lot of this between internal and external pip. Some wait until after external pip to do this. It is really hard to judge when helping one has much chance of success. Usually you do more harm than good. Trust me. I understand your frustration. Most of us have been there.
It's possible it could have something to do with the parent flock but I'd think not likely. Four days is not old for eggs at all. You can go a week without any problems, even if you don't turn them during storage. You do need to watch and not store them too hot. You may have shaken them up on the way home but other than that I'd think it is more likely an incubator problem.
Have you calibrated your thermometer so you know what you are dealing with? Sometimes those pre-set incubator thermostats can be off and regular thermometers can read wrong due to manufacturing tolerances. The incubator being too hot, especially in the first week or so, could cause then to die in the last week. This might help.
Rebel’s Thermometer Calibration
http://cmfarm.us/ThermometerCalibration.html
Rebel’s Hygrometer Calibration
http://cmfarm.us/HygrometerCalibration.html
Another thing that might cause that is not turning them, especially in the first week. That first week is when most body parts are forming. If they are not turned, body parts can form in the wrong place. Most of these chicks die in the shell in the third week.
There are lots of other things that could be causing your problems. I sure can't diagnose it across the internet. Hopefully you can see something in that link that can help.
Good luck!