I would characterize that "motion" the hen is doing as a "hard swallow", which fits the idea of an impaction or something interfering with the food moving down the esophagus and into the crop and beyond. She is using her neck muscles to help the food move down since her normal swallowing motions are not normal/ able to move the food by itself. Sometimes with a chronic impaction or pendulous crop the muscles get stretched and don't work well anymore. Even if you remove the impaction (and my vet once took a huge mat of grass out of a crop surgically - no way it would have moved on its own!) you also have to reduce the luminal size of the over-stretched crop because the flabbiness of it will predispose to repeated impaction.
