They are pups!!!!
Even the best LGD's can play with a chicken to death as a pup.
Two of my Great Pyrenees pups love to chase the chickens when they are bored. Most of the time, they don't pay any attention to them. Great Pyrenees are said to not be reliable until they are 2 years old.
We are working with our pups. As they grow up, they usually stop that nonsense. My older ones have stopped chasing, but still like to run through them and watch them scatter. I have to show them any new additions, though and let them know they belong here.
LGD's still need training.
Now, I understand yours are a German Shepard cross with a Pyrenees. You have a little more work ahead of you.
If you are willing to spend the time, I'm sure you can train your dogs to leave your chickens alone. I believe females are a little harder to train, I think it's because they are more intelligent!!!
I am not a dog trainer, but I believe in the old saying:
If there is a will, there's a way.
It sounds like you are on the right track with taking them into the chicken pen with you on a leash. It is just going to take a lot of time and doing it every day.
In my opinion, the best training is to have a hen with chicks. Put your dog on a leash, take it to the hen & let the hen whip the snot out of the dog. Say your command to the dog while it is getting flogged.
They remember that lesson very well. That is what I do with mine, if I have a hen with chicks, besides using the command I use for them to leave things alone.
Good luck, and I hope you can keep your dogs, they are very pretty dogs.
I'm not a fan of the shock collar. And I'll leave it at that.
Jean