Regarding Dawkins' working definition of the word 'faith' as used by most believers, I would suggest he is confusing the term with blind faith. This notion of blind faith (as far as I can tell) asserts certain things without evidence and "in the teeth of evidence", to quote the man. Dawkins goes too far in presuming this is how all religious believers think. But I don’t think he does this across the board, he reserves his accusations of blind faith to those believers who fit the criteria, he knows that others believe for actual reasons and because of positive evidence. Like him, I do think these believers deserve less respect if they choose the word faith to describe their position. I’m not sure what it should be called, but claiming to have evidence or reasoning for what you believe means you don’t need faith. It becomes provable.
But I want to press you a little further on your equation of faith as being "the sum of all evidence, experience, and logical thinking regarding the Christian god" (correct me if I’m wrong here, but that does appear to be what you are saying). If this is what you mean by faith (you call it "trust") then you will always be on shifting sands. I fail to see how you can call the collection, collation, and weighing of evidence the obviously incorrect term "faith". If the process you use (evidence and reason) has lead you to believe there is a god, then don't call it faith. Call it something else because otherwise you muddy the waters too much. Dawkins only addresses the common definition of faith (as the apostle Paul described it "...in things unseen") rather than Swinburne's version that would have him constantly readdressing a slightly altered idea as new opponents arrive. To explain it another way, I do not need faith when proposing that atoms make up matter. All I need to do is test the evidence surrounding the atomic theory and accept it if it explains what I'm seeing in the best way. No amount of faith is necessary nor would it change the facts on the ground. If you call the testing of evidence surrounding god your faith, it is more appropriate to accept the “theory of god” surely than to use the term faith. But I’m repeating myself.
You say, "but Dawkins et al claim that faith means setting aside any notion of rational warrant for one’s beliefs – and this is a demonstrably false claim"
But how is this so? As far as I can see, the notion of having faith is getting to the point in the journey where rational inquiry and evidence is not forthcoming. If these appeared we would call it science or empiricism, not faith. Having faith does not mean, as you are right to point out, that one 'sets aside' reasoning. In that scenario, there simply isn't anywhere left to go with one's reasoning, and so you need faith. Hence the reason the old phrase, ‘leap of faith’ is neither negative nor positive, but a verb regarding a necessary action. Please advise if this is incorrect.
You say, "I don’t see why the mere fact that people’s apparent experience of the natural world precedes people’s apparent experience of God should make the latter experience suspect."
To someone like yourself I can see how it would be difficult to view the world without any supernatural aspect. It's not so much that the material world works beautifully by itself but the miracle, as Einstein pointed out, is that there are no miracles and the world ticks on using natural processes. You see, you can inject your god in there if you like but the deity appears completely unnecessary for the universe to function. Disregarding a few 'unknowns" such as the beginning of time and space or the origin of life (amongst others) the universe just doesn't require any intervening hand nor any guidance from a celestial being. The idea of a god is simply unnecessary and completely subjective. I will stand by my statement that the natural world is prima facie and the idea of god is suggested to an infant or adult proceeding first experiences, it is not intrinsic. The idea of god is told, passed down, inherited if you will, through conversation and verbal cues. It is far from obvious in the natural order, this assertion is reinforced by a glance at many animist or polytheists living in sodden jungles or sweeping plains. They do not ‘see’ this god by themselves as a child does not ‘see’ it. Besides, if the natural world is not the objective base foundation for perception then which religion objectively replaces that role?
I'm only reticent about calling metaphysical naturalism 'true' because I view the term ‘reality’ as a synonym to the natural order, whatever that means. This in part answers your very last question regarding my personal nomenclature. I am only an atheist in the sense that there has been no evidence provided me to unambiguously show the existence of a deity. I hold that the possibility indeed remains but I have no reason to believe in any god (hence my soft-spot for deism). This is why I view the supernatural as a human addition to clear reality rather than the cause of it.
I will definitely refute the idea of the world looking designed by saying that it is absurd to pronounce such a conclusion using an n size of 1. We simply have no other world or universe to compare to make that assertion (yet). The appearance of the universe and the world as 'designed' is entirely subjective and far from a reality in any sense of the term apart from personal. It's not that naturalism is a simple explanation it's that the supernatural is an exorbitantly unnecessary and redundant explanation. I thoroughly concede that naturalism may not have a "significant explanatory value of adequacy" but simply not feeling good about the conclusions, meanings or implications of a view does not make it incorrect. The world has currently about 560 billion tonnes of life. This is compared to the total mass of the earth 1,877.29 Billion tonnes. Giving it figure of approximately 9% of the earth’s mass as life. If you think that this proves life is fine-tuned or designed for this earth, you’ll also agree that finding an a group of iron atom in a rock the size of Russia is proof that the rock is designed to be a Ferrari. The numbers are even smaller if you take into account our solar system’s planetary mass. And as for the assertion that this planet is 'designed for human', don’t even get me started on the amount of humans compared to cynobacteria...
I would also challenge you, as mentioned somewhere above, to point out the convincing proof that your particular god or supernatural view is responsible for this so-called "going with what we see as being real". If there is such obvious evidence for the truth of the supernatural then why are there so many differing opinions about god, each opinion holder grasping as tightly as the next to their particular views on religion?
But this also partly answers your musings on the validity of personal experiences. If you think, as you must, that your own experiences and those of others with a similar mindset provide validation for your god or religion then you must also take every personal supernatural experience as positive proof for their respective experiences. Otherwise, give me a cogent reason why your experiences outweigh those of others' (and specifically a criterion to objectively perform an unbiased test to establish the validity of your claims). I am forced to say that claims made without supporting evidence can be dismissed without supporting evidence.
Naturalism does carry the burden of proof, no doubt about it. This doesn't surprise me in the slightest. The difference between the supernatural and the natural lies in the eminent testability of the latter and the total lack of detection of the former. This is where you and I depart. I have no issues with the testing of the natural world because so far as we can assume, it exists; it's the supernatural world that needs to be definitively uncovered and that fails the burden of proof. Naturalism succeeds because everything that we experience through our senses in this universe stems from natural causes. Any recourse to blame supernatural causes only stagnates progress and kicks the can further down the road. Indeed, as history shows whenever we've thought an event was the responsibility of this or that godhead it always turns out to be of natural causes. There's an old saying that goes, "Before you assert that an event was out of this world, make sure it is not of this world".
No, my assertion of a claim-less atheism does not make it equivalent to agnosticism (a slippery term at best and one that supports atheism rather than theism, also sometimes called 'weak-atheism'). I am an atheist because I say no convincing argument given nor any evidence presented has ever established the existence of god/s. I can only speak for myself when I say that I am open and willing to change my mind if sufficient evidence is provided. This is a difficult target to hit for a supernatural entity though, because as the classification belies, any interdiction or presentation from this being would require it to follow natural processes in order for me to experience it. This action immediately shoots the supernatural deity in the metaphorical foot by transforming the supernatural into the natural, making any evidence for the supernatural definitively impossible. I'm sure this god could think of something to get around this dilemma but I would be simply imagining things, making stuff up in other words.
A convincing argument for god is not entirely a different story however. Plenty of people have made rather good, cogent syllogisms establishing their god’s existence. I would suggest however that no mammalian primate could ever claim to know or prove the existence of a supernatural being on principle. Further, any Christian's claim to prove the existence of their god by argument ultimately achieves nothing and is worse than futile. All their work lies ahead of them still to prove their personal, interdicting, miracle-working, son-sending god. All anyone can ever do with argument is to make the existence of a deist god appear at least plausible.
I will peruse your archives and read more of your opinions about theological matters though, for sure.