Ok, I'll tell you what I would do....as a first step before considering anything more invasive.

You say you noticed a response to antibiotic treatment I would ask vet to put him on a stronger course and see if this works. From what you describe ( timing of head shaking ) it does sound to me as if something is irritating/causing him pain. I would have liked to have seen the response to the ear drops-it's a pity you had difficulty administering them but it's the same with most cats!

The other thing that struck me was the blood in stools. Sounds as if he has colitis-a form of IBD quite often a symptom of an allergy to something in the diet ie grains in cat food. Is he on dry food by any chance? Alternatively, parasites can be a cause so I'd worm him if not up to date.I wouldn't leave that untreated and I'd mention this to the vet. Pro-Kolin is very good in treating it-if parasites not the cause! Colitis might explain his unusual toileting habits as well!

I hope you find a solution soon!