My thoughts on this:
1. After you admitted the mistake, you were almost surely going to get some sort of punishment. Personally I would have just demoted you.
2. Your goal is to control the situation by taking the initiative and offering up a lesser punishment that shows you want to atone, but doesn't make you (or the Empire) look weak, and, perhaps more importantly, strokes the Emperor's ego.
3. Given the above, instead of surrendering to the Tribunal, I would have surrendered myself to the *Emperor himself* for punishment. Emperor doesn't care if you broke Tribunal law per se; he cares that you broke *Imperial Law*. If he's in your PK, let him kill you. If not, then offer to submit yourself to be executed by the Imperial Council.
Instead of the above, another approach is to just lie. Trick is you have to make it convincing. In this case, I might claim that the conjurer attacked me first, in town, and the Magistrate didn't hear. Then he fled, ran around town, I caught up with him and tripped, but by that time a Magistrate had come on duty and I was the one who got flagged.
This is a total lie, of course, but it might be believed.