Arse over .... Thanks for your observations. My feeling is that the expression is flexible. Several variations come to mind. I did not invent "arse over elbow". I cannot remember who used it in my presence. But it appeals because of its graphic potential, suggesting a chaotic tangle of limbs.
Although I do not as a rule make a habit of discussing complaints, I should now add that the stiff neck which has features here and elsewhere, returned with a vengeance as I began to recover from the flue. The result: a human lamppost. Rigid neck muscles are now gently relieved by pain killers and anti-inflamatories, add a new and painful dimension to the sick room. Enough.