@Quid est Veritas?, you actually wrote many things that I have to actually agree with most of your points, only I did not understand when you said: "Science arose in Western Christendom."
I think it is incorrect to say that without the presuppositions of Christianity modern science, morality or anything else of the sort would not exist, then it means that science works only because the "God of Christianity" proposed this laws? It is true when it says that science had a revival in Christian Europe, however, the Renaissance was a revitalization of the classical Greek and Roman principles, and a break with the theology of earlier centuries as you yourself suggested. Of course, even if it were true that modern science has its origin in Christianity, none of this advocates in favor of any religious doctrine, because with Christianity or without Christianity society would evolve into knowledge sooner or later. I hope I did not misunderstand.
Let us first get our terms straight. What is meant by Science? The term can be quite protean, with layered meaning, from broad popular usage meaning basically knowledge or 'fact', to more technical and correct usages. Generally, I mean a systematic body of empiric knowledge derived via Scientific Method, by the term. Science is grounded in Scepticism, that all discoveries have to be reproducible, have to be doubted.
So Chinese invention of gunpowder was not scientific, as this was done around alchemical practices looking for spiritual harmony and utilising concepts like Li. It was not systematic, nor empiric. Similarly it would not be falsifiable and the validity of the thinking leading up to the discovery, was never called into question.
So by this more proper definition of Science as it functions today, the only time it arose was in Western Europe - specifically in the 12th century from the work of Roger Bacon and Grosseteste.
Proto-Scientific systems which we can perhaps also grant the term, being Sceptical, Empiric and Systematic; though without the formal mechanisms; can be granted to the Transoxianian Islamic flowering and Hellenistic Natural Philosophy, the latter from which both of the former ultimately derive.
Now what do we need for Science? It requires a number of assumptions:
1. The belief that data is reproducible, that if something is done a hundred times, that 101 and on will yield the same result.
2.That Empiric evidence at least reflects something tangible (unlike Buddhist, Taoist or Eleatic schools that deny fundamental reality to the empiric, being Void or so, with some form of non-duality being 'real').
3. The belief in Intersubjective value, that two people would experience the same thing in similar ways.
4. Belief in causation, that everything can be explained in terms of Causes leading up to it. That events or such, don't occur spontaneously (as opposed to Taoism or Karma, that seek explanations outside actual physical events).
5. Ex nihilo nihil fit - that nothing just pops into existence, but has been transformations of what came before.
6. That the universe is ordered, and works by fixed laws that can be articulated and understood by humans.
ETC.
There are many others, some more or less important, or more or less relevant. For instance, denying creation from nothing is excused for Creation by traditional Scientists (being a Miracle, and thus per defitionem outside the realm of Science) or for certain interpretations of the Big Bang Theory, now that solid state universes have fallen from fashion. Or the 'popping into being' of quantum particles.
So it took 1800 odd years of Western Philosophy to articulate and argue all the positions for Science in its modern form to exist. This is based off Aristotle, who held to systematic classification and enquiry, and that all had a cause. However, a lot of the requirements are inherent theologic positions of Abrahamic religions - an ordered, intelligble universe with human spirits being separate in some sense from the matter, etc. Nominalism also played a part.
So historically, Science arose once - amongst mediaeval Franciscan monks and propogated through Christian Europe. Islam in Transoxiana came close, but it petered out. Both based off of the systematic, sceptical and empiric traditions of Greek Philosophy, which however never gained the upper hand in antiquity. This was likely cultural too, as there was no agreement that the world need be knowable, nor that knowledge can even be in some sense accrued.
The Renaissance quickened the pulse of Science through the rediscovery of the classic sources in their original Greek form; and from the New Philosophy of Francis Bacon onwards, Science cut a few of its Aristotlean roots (only often to make its way back again, the long way round). The underlying assumptions of the validity and nature of an Empiric world remain, grounded in a methodologic Naturalism that seeks causes and not assume the miraculous.
So Science could certainly have arisen without Christianity, even without an Abrahamic God. But it didn't, and the theology of Abrahamic Religions is well suited to support the necessary assumptions that need to be made to allow Science to be. No other society even came close, and based on the worldviews within said societies (Karma, Confucian Li, Shinto Musubi, etc.) this is no accident. So it would be exceedingly unlikely in my opinion, that it would have. The world stayed largely the same, punctuated by one or two important discoveries every couple of centuries, till Western Scientists sat down and began systematically trying to understand what is going on. Thereafter, change came thick and fast. It was helped by a 'sense of the past', that change and improvement was actually possible (as opposed to Chinese beliefs that yesterday will be the same as tomorrow under Heaven or cyclical Hindu concepts), built into the Christian idea that we are moving forward in a narrative, that there is an ending. For Progress to exist, there must be something to move towards, and not just be cycles and stasis.
Most Scientists in history were Christians, some highly devout like Newton, Mendell, Priestley, etc. who often hedged their ideas on their theology. Newton spent years investigating Revelation, and wrote how it impacted his understanding of Mechanics, as an example.
Today we learn Christian concepts as we grow up, from our culture and society; such as linear time, or an ordered knowable world. Don't assume these were universal, for they certainly weren't. They are assumed cultural baggage of our new crop of Atheist Scientists, but are by no means self-evident universal values. Empiricism is not a natural human state - it needs to be taught. There are fascinating experiments to this effect, called the Princess Anne experiments, that you could look up.
If you cut the silver thread that connects the Sciences to Abrahamic religious theology, then a lot of your philosophic foundation falls apart, and you are left having to make massive axiomatic leaps of faith to support the edifice of Science. The denigration of Philosophy on the altar of what is 'Practical' or 'Pragmatic' is the result, as Scientists don't want to address the fact that they are making assumptions themselves, when they pride themselves on being Empiric. Even here though, a lot of Theoretical physics has moved away from Scientific Method entirely, so we may be looking at the twilight years anyway.
I hope I managed to answer your question, but without Abrahamic Theology, the cultural groundwork for Science to come into existence simply is not there. 5000+ years of Civilisation never led to it, in multiple forms, and in quite advanced and sophisticated societies, without that background. Likewise, it is now established in our culture, and other cultures that adopt Science are in essence Westernising thereby, but with growing relativism in our society driven by its secularisation, Science itself is in trouble - look at Transgenderism and seeing Biologic Sex as merely a human construct, or the Antivaxxers, to see the type of problems that lie ahead for Science on account of this.