If there is no doubt that the student "spontaneously" threw their shoe from the 5th floor and that it hit you that day, then your argument is that it was an accident, it happened, however there has been no recognition by the organisation about the repercussions on you personally. It has massively impacted your health and you've suffered a loss of livelihood.
Was any action taken to discipline the student either at the time or afterwards when you had to be signed off with headaches?. Do you know the identify of the student who did it? Not suggesting full on retribution, but you should be bringing the situation into a sense of reality, in terms of what happened and how it has affected your life. Plus the fact, you have now got your health problem under control and would like to work with them to arrange a phased return.
Could you write a suscinct account of the above, and send it to HR.
I think so much detail over a long period of time has subsumed the key issue, which you could summarise. Ask the direct question in writing, based on the facts presented, would they reconsider and let you return to work.
If there is no movement by them, then at least get them to provide a good reference due to your hitherto unblemished work history with them. And move forward. I'm sure there is a strong demand for TAs atm.