Hi NakedNeck, I might have a lead for you that could help your bird. I'm new here, and I don't know much about poultry yet (horses have long been my thing), but a friend of mine commented recently that her tom was doing something very similar to what your hen does. She said he does it every night without fail. In looking for other information, I stumbled across the term "stargazing" in regard to turkeys like this. There's a long proper name that begins with the letter "O," and it seems to have several schools of thought as to why they do this. For some it's a B12 deficiency; for others it's a neurological symptom and is found in neglected birds. There were other possible explanations, none of which I can seem to remember right now. *sigh*
I know about enough to be dangerous, so I thought I'd just offer that you google "stargazing turkeys" and see what comes up that might fit your situation. I hope this helps you find answers.