Question: Is there a way to answer the apparent difficulty between the Avnai Nezer and the Nimukay Yosef? It seems that rov shitos hold that the entire baking process must take place on shabbos, and, as you pointed out, it is apparent that Rashi held so too. Therefore it would be important to try to answer up the difficulty between them and the famous quote of the Nimukay Yosef.
The Nimukei Yosef means that a fire that burns on Shabbos as a result of one's action on Erev Shabbos is not considered as being constantly renewed by one's action on Shabbos. Rather, one's action yesterday (Erev Shabbos) is viewed as the cause of everything that occurs as a result of it on Shabbos. That is, the burning of the fire is considered to have been caused by his action yesterday and not by any action on Shabbos. Of course, the fire itself is burning on Shabbos, as is apparent to the eye.
If so, it could be that with regard to baking on Shabbos, indeed the action (of placing the dough into the oven) is performed on Shabbos and not on Motza'ei Shabbos and nevertheless he is Patur, because we do not make a person Chayav on an action of cooking that was completed after Shabbos. After all, our eyes see that the cooking was not completed until after Shabbos.
Daf 4a: I don't understand why there is a question -Are we allowed to transgress the Rabbinic Law of Removing The Bread in order to save someone from being killed by Bais Din in a case where he put the bread in the oven on purpose- Why dosen't this fall into the catagory of Saving One's Life where we are permitted to put aside even Biblical Laws?
First, he would not actually be subject to the death penalty here, if the bread was not removed, as Tosfos points out.
Second, in general, when a person transgresses a Torah prohibition that is punishable with death, shall we say that he should not be killed because of the rule that saving one's life overrides the laws of the Torah? Of course not! The reason is because the Torah commands us to kill him, and since he knew that the Torah so commands ("Hasra'ah," giving him warning before he does the transgression, is a necessary condition for giving the death penalty), and yet he still transgressed the prohibition with full knowledge of the consequences, he gets punished. The same is true here. The person put the dough into the oven after having been warned that baking on Shabbos is forbidden and carries with it a punishment of death.