Probably some spoilers but I think there is 3 major things that MC can literally say to prove his innocence: (Spoilers)
- 1: Even if he was on the scene of the tragedy, he was way to clean to be a culprit you would imagine if MC did it why is he too clean?
- 2: If they checked the body for Rigor Mortis and Wounds. It would be helpful I even imagine it like a Danganronpa Trial where the MC was to prove his innocence by saying: "If any of you had checked for the time of death you would notice that was before I entered the room".
- 3: Them the fact that the MC was literally sick? and there was many at list 3+ that can affirm that is in fact correct due to the fall. And the fact even on the day of the tragedy the MC wasn´t feeling well would be enough prove to his innocence if the above wasn´t checked. Sure, he only did feint when saying what he had dreamt the day before. But even thou he wasn´t in a good shape to commit the tragedy...
With that I probably have proven the fact that if the MC was smart, he would probably survive the trial without being executed, it probably would be fun that you´d have like multiple choices and had to select like: (A: Sick | B: Weapon | C: Lack of Blood on Clothes)
Sure, it would be tedious but basically if done correctly would be awesome. I´m basically just wishful thinking but if needed I could make a small example.