Though I really don't understand the necessity of this argument, to ruminate, circulate or redefine god, I should tell you the story that humankind wanted to survive, so they started to think about death, and consequently dangers: the things which kill us. When we reached the level of causality, the question was what's the cause of an earthquake, rain, volcano and so on? So we came up with many goddesses of which the Abrahamic god is the common denominator.
So far, we've just named the cause as you did: "It is important to put God in at this level if we wish to express our beliefs and be consistent with the current state of scientific theory. For me, I would prefer to think of God as being innate to all matter" and there's no problem with it. At this level, there's no harm to define the existence of something. It becomes dangerous when we try to anthropomorphize it, not like the Greek Gods or the idea of the old man, but when as you said we "hunted for the higher order" which is assuming that god has intention or purpose. So, we thought that since humankind reaches the ultimate cause which is planning and purpose, the nature or god must have a/the purpose too. That's where, in my opinion, we went wrong and this idea has caused more harm than benefit.
This is gonna be a long story that I am telling in my blog. So, to wrap up here, I should say that there's no problem with defining god as the cause of formation of molecules or the whole universe, but this definition is barren because with which we can't predict anything. The difference between the two statement, God changes everything and force changes everything, is the second can be formulated, hence be applied to predict the moment when the Mars Rover would land on Mars.

I'm not sure but I think Karl Popper once said that "God exists" is not a statement because it can neither be proven nor falsified. That's why, in my opinion, any argument about the existence of God is futile.

Both Even and Natural numbers are infinite. Are they equal?