I am sorry to hear it has taken this long to get to a hearing and that things are not going well. I will definitely be hoping for the best.
I can tell you about my experience....
It was 36 months before my hearing. I received a favorable decision from the court hearing and their approval a month later from the hearing, and then I received a lump sum check for the total back benefits and for the current month SSDI two months after I received the favorable decision. The attorney fees were already withdrawn from it. I don't know about the payments being divided into 1/3's. This may have changed since my award and if so, I apologize that I cannot answer your question about this as to when or how they might be divided.
Be sure though come tax time to know that you will need to refile taxes for the years of back payment if you received any other taxable income during that time; otherwise it appears you received all that income for the wrong year or all at once as oppose to throughout that time had it been awarded, which would have been in the appropriate years, for those years also including the attorney's amount (even though you did not technical receive the attorney's fees, this was awarded to you and counts as income.) It would be best to consult a tax preparer/specialist to be safe regardless.
My SSDI monthly started with the back payment check and from that point forward. I did not qualiy for SSI so I cannot answer what happens with SSI. I am sorry.
Again, hoping for the best for you and hang in there.