Theists aren't very good at arguing their case, not least because they don't really have one in the proper academic sense of the term, but also because it's really something that they didn't have to do until comparatively recently. The traditional theist stances towards anything that questioned their beliefs were normally either condemnation or simply ignoring the opposition.

I've been criticised on this site before for using the term "schizophrenic" to describe the religious mind, but I persist in doing so since the term - whatever its medical employment - literally means "divided mind", and if one does not proceed from that assumption when arguing with a theist then the experience is bound to dissolve into frustrating illogicality very quickly. The division is more obvious in some compared to others but in my experience it is present always, and becomes most evident when they start to employ "rational" explanations for their unfounded beliefs. When you realise that your interlocutor is taking the liberty of jumping at will between two oppositional mind-sets then, while their arguments don't get any better, at least you can see where they're coming from - two places at once.

What is divided is the part of the mind that has been conditioned and trained to think logically from the more instinctive part of the mind which has the ability to jump to quick conclusions. Both have a role in survival, of course, but religious belief tends to be rooted in the latter while retaining an ability to monopolise the former when it comes to justification. Dawkins's use of the term "delusion" was therefore spot on - it cannot be anything else.

An honest theist, when pressed to explain why he or she persists in a belief for which there is no evidence will say "I don't know". They will also readily admit that the form of this belief that they adhere to is of course decided as much by the geography surrounding their birthplace as the defendability of its tenets. But honest theists are seemingly hard to find, at least in those terms. The dishonesty in not making these simple and obvious admissions is compounded when the delusional aspect to their condition encourages them to attempt to justify their stance employing rhetoric and processes normally reserved for more practical purposes. They call it theology. I call it hyperbole in the Aristotlean sense - the intentional exaggeration of one or more semantic norms at the expense of others. Rhetorically it is used as a technique to deflect attention from an argument's weakness by emphasising an apparent strength and then quickly moving on before it too can be analysed and revealed as evidence for the dishonest intention behind its use.

The rhetorical answer to this technique is well exemplified by several of the site regulars here. Users of hyperbole simply need to be brought back again and again to those things that they present as their argument's strengths and forced to demonstrate that strength - something they are rarely able to do. If a person is being intentionally dishonest the technique pays dividends very quickly. If, on the other hand, the arguer is delusional and especially if they are religious delusionals, then the technique simply sends them skipping back to the instinctive - where "it is right because I say so" actually makes sense, at least to them.

Pointing out ways in which theists could better argue their case is therefore rather pointless, if the hope is to improve the debate and therefore improve the chances of rescuing them from their delusion. My own experience is that the only reasonably effective way of helping them address their delusional condition is to attempt - through whatever rhetorical device applies - to keep their brain working in the "logical" sector and purposefully haul them out when they retreat into the instinctive, when for example words like "mystery", "holy", "spiritual" etc begin insinuating themselves into the logical flow of the debate. But to do this effectively it is vital to focus on those arguments that they themselves retain the ability to understand and follow, and not introduce others which they themselves did not derive from deduction. You just build another bridge for them to hop over and back into the irrational and instinctive region of their mind, since the source of the theist mind-set resides there and all new arguments - indeed all new facts - undergo that negative filtering for as long as the delusion is harboured.

I like your "survival of the most stable" explanation and I'm sure there are several different angles to defeat the theist argument. In regards to dualism, this frankly is a childish rejection of overwhelming evidence in neuroscience that all aspects of the mind including consciousness are the result of the neurophysiological activity of the brain. Dualism has as much validity as believing in Santa Claus or the Easter Bunny. If Wernicke's and Broca's area are permanently damaged then that individual has a permanent language impairment (ie. an aphasia). A dualist claims that the soul still possesses language. A person who has irreversible damage to the bilateral fusiform gyri will be unable to recognize previously familiar faces. Yet the dualist claims that the soul will recognize family members in an afterlife. A dualist claims that a person with advanced Alzheimer's disease has a soul that can think rationally with an intact memory. And goblins live in my attic when no one is looking and fairies live in treetops. Dualism has absolutely no supportive scientific evidence and is among the dumbest arguments for the existence of God and very similar to the introspective argument of "I personally feel the presence of the Lord" as being evidence. Any theist who seriously wants to make the case for the existence of God would be on very shaky ground using the dualism defense.

The golden rule for debating with a theist is always to follow his or her assertion with the question "On what evidence do you base that?" This will either elicit another assertion (against which your question should immediately be employed again) or something that is not evidence at all. In a formal debate it is a matter therefore of note-taking and writing down every assertion during your opponent's allotted speaking time. If your research is even half good you can destroy their testimony with logic blindfolded. Of course whether you convince your audience is a moot point, but that's true always. Most of them arrive predecided anyway. Also (and I've noticed this with some of the RRS interviews and debates) you run a real risk, having deduced how flawed your opponents' stance is and therefore vulnerable to logical assault, of sounding disinterested or smug with your rebuttal. This can potentially piss neutrals off who are following the debate and lead to votes against you on the day.

It is far more difficult to engage in debate with a scientific mind since you must assume that any assertion made does indeed have at least some form of justification based on empirical testing behind it, even if he or she mightn't be familiar with it. However a scientific mind employed to defend theism is probably the easiest to defeat in debate since your opponent knows full well when he or she has stepped over the line of logic and will often do half your work for you in attempting to belatedly dress assertion up as fact. Sometimes it is simply enough to repeat their statements and invite the audience to consider them again. Rhetoric is redundant when someone is hanging themselves, as Cicero once said, you need only to feed them more rope.