You've just described at best, a mechanical universe, and at worst, a static universe. Your statements also contradict themselves. If God is unchanging, God could not possibly always do what is best for us, because we ARE always changing (unless, of course, we want to throw out any concept of free will, and thus posit that we are mere cogs in a machine, and what we experience is all illusion). The idea that God transcends time really doesn't help here, because God always "doing" for us necessitates entering into time.
There is a way out, though. A God that is changing and unchanging could always do what is best for us, because we are always changing. This is called a relational universe; it is dynamic and more closely resembles the Bible's COMPLETE depiction of God and our experiences.
BTW, I think there may be a few Christians out there who believe Christ suffered on the cross, and that God grieves and rejoices with humanity and for humanity.
God is not the universe. He exists apart from it. So, He created a universe which is meant to grow in its ability to glorify God.
Man, the height of creation, is likewise a creature that grows towards God like a vine grows towards the sun.
Time is just as much a created thing as a rock or you and me. God exists outside of time. Thus, His relationship towards us does not change, even though we change in our relationship towards Him.
As for your last comment, it introduces a paradox (a seeming contradiction):
God does not have a body.
Jesus is fully God.
Jesus DOES have a body.
Jesus is one Divine Person having two complete natures.
The human nature Jesus possesses is not intrinsic to Who He Is. Jesus doesn't *NEED* the human nature, He just happens to possess it.
How does this work? The single Divine nature consists of the Divine Intellect and the Divine Will. A complete human nature consists of a human body and a human soul. The human soul consists of the human intellect and human will, so human nature = body, soul, intellect and will.
The one Divine nature does not change.
Human nature is meant to grow and change, it is capable of suffering.
There is only one Person in Jesus - the Son of God.
However, since Jesus possesses two complete natures, He is the only person in existence who possesses two intellects (the Divine intellect and a human intellect) and two wills (the Divine will and a human will).
Thus, while the Divine nature He possesses does not undergo any change (and therefore doesn't suffer), His human nature is absolutely capable of suffering, weeping, laughing, etc.
Because the Person of God possesses this intrinsically unnecessary but still fully functional human nature, we can say "God suffered and God died on the Cross": His actions are "theandric", that is, they have the nature of human actions, but - since those human actions are joined to the divine nature - the human actions are capable of being attributed to God.
We must simply keep in mind that when we attribute a human action to God, that this human action is not intrinsically necessary to Who God is in Himself since the human nature is not intrinsically part of or necessary to the divine nature.
So, yes, He weeps with us, grieves with us, suffers with us, dies with us and resurrects with us, but at the same time He does not change in Himself.
This is why the Incarnation is the key to everything. If God did not take on flesh, then the Deists would be absolutely right. But since He *HAS* taken on flesh, they are absolutely wrong. He injected Himself into time while simultaneously remaining outside of it.