It's easy to overstate the relevance of Nietzsche's pronunciation to the terms of classical Theology. When Nietzsche talks about God, he talks about God as a cornerstone of Western Culture, not God as the character of a Christian story. From section 343 of TGS, Nietzsche spells out his intended meaning:
The greatest recent event - that God is dead, that the belief in the Christian god
has become unbelievable - is already beginning to cast its first shadows over Europe.
Throughout Western history, belief in Christianity was not merely seen as True but as a necessary prerequisite to any kind of civilized culture. It might seem hard for us to think now, given that we seem rather accustomed to a kind of capitalism-driven hollowness underlying the notions of Globalization, but Europe and its colonies was very much founded on the idea of a principled providence, that the West carried the truth about God and that its spread across the globe is that of Divine Right. Sure, this made empires very wealthy, but that was proposed to be simply reward for the elect and confirmation of their faith, rather than the purpose behind a protracted and vicious campaign of motivated subjection of others who lacked their technologies of power.
Nietzsche addresses the death of God in such terms - namely that given the mass of evil and suffering that has befallen the world in the actions of a humanity spurred on in this way, there can be nothing left of Him now. Whatever Christian theology might claim of or about God in metaphysical terms is not specifically his concern, because the evidence is clear - we are monsters, and whatever abstract right to rule that we proposed God bequeathed upon us as his servants has clearly been jettisoned in our rush to bring the sword.
In the process of the Enlightenment, of Secularism and Science, the truth of this has started to become clear, and the utter fallacy of Christian imperialism leaves us in a state of not merely uncertainty but of profound ending and absence. The Christianity that grounded our world's actions is what we do in fact believe about God, and the Redemption and ultimate Salvation that it offered us is part of why we as a society did what we did to the rest of the world. We have to face up to the reality of what we have done, and to claim that either that self-same God lives on or that he forgives us is an act of escape and pretense; our task is to try now to find some way to live on past it in the cold void of a God that no longer defends or supports our collective action.
Can we say that God's death was freely chosen? Christ, perhaps, took his choices into his own hands and acted with authenticity, but God's death seems to have been violent and long drawn out by a Christian West that scraped his bones dry for every ounce of empowerment we could find.