The idea that the world makes sense is expressible without any reference to God,
I'm saying that the belief that the world makes sense is equivalent to belief in God. When you think about it, the idea that the world makes sense is just a strong a statement as the existence of God, and just as unsupported.
and the word "God" is commonly used to mean something else.
I don't think so. I'm convinced that atheists (especially New Atheists) have a distorted, narrow idea about what the word God means. Problematically, many theists also have unsophisticated or inconsistent ideas about God. Often they confuse concrete analogies of God with actual descriptions of God. This is a serious theological error (idolatry).
To argue that God exists, you don't need to argue that every conceived idea of God is true. At its fundamental theological roots, the Judeo-Christian religions assert that God is indescribable and not anything you can think of ... so Dawkin's God or whatever you're thinking of isn't the right description either. I'm sure this sounds very much like defending God behind refusing to define God but, personally, I wouldn't expect the theory of everything to be a concrete, describable thing. I would expect that it is highly interpretable and vast in some sense. For a religion, it is enough to have faith in the possibility of a theory and try and sort out (through intuition, experience and 'good epistemology') what kinds of things you can know about it.
Judeo-Christian religions assert that God is indescribable and not anything you can think of ...
This is certainly not my understanding of the Judeo-Christian concept of God, and I spent 12 years in Christian education (believe me, I am not bragging when I say this).
God was supposed to be something ''mere humans'' could reach by the proper application of logic. Your description sounds much more like the purely transcendent Muslim concept of God, according to which God didn't even have to obey the laws of logic, causality, or his own commands.
One occasionally sees such remarks as, "What good does it do to go around being angry about the nonexistence of God?" (on the one hand) or "Babies are natural atheists" (on the other). It seems to me that such remarks, and the rather silly discussions that get started around them, show that the concept "Atheism" is really made up of two distinct components, which one might call "untheism" and "antitheism".
A pure "untheist" would be someone who grew up in a society where the concept of God had simply never been invented - where writing was invented before agriculture, say, and the first plants and animals were domesticated by early scientists. In this world, superstition never got past the hunter-gatherer stage - a world seemingly haunted by mostly amoral spirits - before coming into conflict with Science and getting slapped down.
Hunter-gatherer superstition isn't much like what we think of as "religion". Early Westerners often derided it as not really being religion at all, and they were right, in my opinion. In the hunter-gatherer stage the supernatural agents aren't particularly moral, or charged with enforcing any rules; they may be placated with ceremonies, but not worshipped. But above all - they haven't yet split their epistemology. Hunter-gatherer cultures don't have special rules for reasoning about "supernatural" entities, or indeed an explicit distinction between supernatural entities and natural ones; the thunder spirits are just out there in the world, as evidenced by lightning, and the rain dance is supposed to manipulate them - it may not be perfect but it's the best rain dance developed so far, there was that famous time when it worked...
If you could show hunter-gatherers a raindance that called on a different spirit and worked with perfect reliability, or, equivalently, a desalination plant, they'd probably chuck the old spirit right out the window. Because there are no special rules for reasoning about it - nothing that denies the validity of the Elijah Test that the previous rain-dance just failed. Faith is a post-agricultural concept. Before you have chiefdoms where the priests are a branch of government, the gods aren't good, they don't enforce the chiefdom's rules, and there's no penalty for questioning them.
And so the Untheist culture, when it invents science, simply concludes in a very ordinary way that rain turns out to be caused by condensation in clouds rather than rain spirits; and at once they say "Oops" and chuck the old superstitions out the window; because they only got as far as superstitions, and not as far as anti-epistemology.
The Untheists don't know they're "atheists" because no one has ever told them what they're supposed to not believe in - nobody has invented a "high god" to be chief of the pantheon, let alone monolatry or monotheism.
However, the Untheists do know that they don't believe in tree spirits. And we shall even suppose that the Untheists don't believe in tree spirits, because they have a sophisticated and good epistemology - they understand why it is in general a bad idea to postulate ontologically basic mental entities.
So if you come up to the Untheists and say:
"The universe was created by God -"
"By what?"
"By a, ah, um, God is the Creator - the Mind that chose to make the universe -"
"So the universe was created by an intelligent agent. Well, that's the standard Simulation Hypothesis, but do you have actual evidence confirming this? You sounded very certain -"
"No, not like the Matrix! God isn't in another universe simulating this one, God just... is. He's indescribable. He's the First Cause, the Creator of everything -"
"Okay, that sounds like you just postulated an ontologically basic mental entity. And you offered a mysterious answer to a mysterious question. Besides, where are you getting all this stuff? Could you maybe start by telling us about your evidence - the new observation you're trying to interpret?"
"I don't need any evidence! I have faith!"
"You have what?"
And at this very moment the Untheists have become, for the first time, Atheists. And what they just acquired, between the two points, was Antitheism - explicit arguments against explicit theism. You can be an Untheist without ever having heard of God, but you can't be an Antitheist.
Of course the Untheists are not inventing new rules to refute God, just applying their standard epistemological guidelines that their civilization developed in the course of rejecting, say, vitalism. But then that's just what we rationalist folk claim antitheism is supposed to be, in our own world: a strictly standard analysis of religion which turns out to issue a strong rejection - both epistemically and morally, and not after too much time. Every antitheist argument is supposed to be a special case of general rules of epistemology and morality which ought to have applications beyond religion - visible in the encounters of science with vitalism, say.
With this distinction in hand, you can make a bit more sense of some modern debates - for example, "Why care so much about God not existing?" could become "What is the public benefit from publicizing antitheism?" Or "What good is it to just be against something? Where is the positive agenda?" becomes "Less antitheism and more untheism in our atheism, please!" And "Babies are born atheists", which sounds a bit odd, is now understood to sound odd because babies have no grasp of antitheism.
And as for the claim that religion is compatible with Reason - well, is there a single religious claim that a well-developed, sophisticated Untheist culture would not reject? When they have no reason to suspend judgment, and no anti-epistemology of separate magisteria, and no established religions in their society to avoid upsetting?
There's nothing inherently fulfilling about arguing against Goddism - in a society of Untheists, no one would ever give the issue a second thought. But in this world, at least, insanity is not a good thing, and sanity is worth defending, and explicit antitheism by the likes of Richard Dawkins would surely be a public service conditioning on the proposition of it actually working. (Which it may in fact be doing; the next generation is growing up increasingly atheist.) Yet in the long run, the goal is an Untheistic society, not an Atheistic one - one in which the question "What's left, when God is gone?" is greeted by a puzzled look and "What exactly is missing?"