I- I refer you to the recent book by Kushner entitled, "When bad things happen to good people". The take of judiasm is made clear in that book.
II- The cruxification of Jesus was an act of god. If the jews helped carry it out, so be it. But cruxification is the Roman means of execution. The jewish method was by stoning. So my guess is that it was the Romans tht carried out the execution, and carried out the will of god as well.
III- You missed the most important comment by god that both sides are righteous and that one carries out the play of life with piety and dignity. Even Jesus said that you should keep on doing what you are doing. That is because itr is all controlled by god. So do not blame a particular religion for anything. All rteligions, especially now, are just carrying out the will of god.
So bottomline, it seems that you have confirmed my view that all religions have considered the basic problem of why bad things happen to good people. Eastern religions, all of them, created the concept of karma to explain that. Judiasm explains it as being the result of past transgressions against god, as you have mentioned in so many words. Christianity, in my view, has no real explanation. In fact, I do not know of any scripture where Jesus addresses that problem, or even Paul. If you know of any, please tell us.
You prefaced this discussion by implying that the cruxification of Jesus was a bad thing happening to a good person. I see that quite differently. It was the will of god to sacrifice his son for the benefit of the world. As such, it was not a bad thing. If you think it was a bad thing, you have missed the whole point of christianity.