I don't know your birds, but if I saw this in mine, it is a cough that they do when they get a bit of food stuck.
That combined with the serpentine neck movements makes me feel that she is trying to adjust her crop and/or has something bothering her in her throat or neck.
How is her crop? How is she eating? Does her crop empty properly, and does she have any issues with eating at all? Make sure it's not a "simple" impaction or sour crop, just in case. At least that is something you can treat.
Make her reach down to the floor for some food (use a treat that she likes very much if necessary). Does she react at all strangely? Does she act woozy?
One of the first organs to get affected with viceral lymphomatic Marek's is the thymus, which is right at the clavicle ... very near the crop. I have experienced birds getting tumors here first, and within days the tumors on the heart were causing his comb to turn deep purple (then blue when he was near death). The lymphomas were very aggressive and rapid.
Marek's really does not follow any rules though, so it might be much slower in your hen.
Or, this might not be tumors at all! It is just a guess on my part!
She looks so sweet. I really hope she gets better. Keep her hydrated and do a very through crop check, would be my best advice at this time.