I don't find "it's different priors" a "rational basis for disagreement" at all! It's merely a conversation-stopper. Peoples' assignments of priors have causal histories, and sometimes even actual reasoning behind them! Find those and at least we can start talking again. Assigning priors isn't some mystical process - probability always comes from the information you have, some people just start with different sets of information.
I read that as the point that was being made - instead of arguing cross-purposes, a theist and an atheist might actually be able to agree that the point on which they diverge is that prior, and then argue about that instead.
"Whatever intelligence is, it can't be intelligent all the way down. It's just dumb stuff at the bottom." — Andy Clark
The problem is that people perceive intelligent agents to be kind of a black box, a cornucopia that can sprout an abundance of novelty. But if you are going to create an intelligent agent, you need a blueprint. Such a design pattern ultimately has to have its origin in unintelligent processes, or needs to be there from the beginning.
I am far from a complexity theorist, so please correct me if I am wrong, but if some things were irreducible complex, then it would not only apply to creations but also to their blueprints. Either the idea for our universe was already given, in which case god would merely be a compiler or executor, or the idea evolved from simpler, or "less complete" predecessors, in which case there was no irreducible complexity. The advance of knowledge seems to be an evolutionary process itself.
Very interesting! I find that a lot of these sort of arguments for God emphasise a certian informal 'it makes sense' approach, where questioning our judgement on what makes sense and exploring why it's there is probably the most meaningful approach. Some are more formalised, though: Plantinga's, for instace, relies on a series of very explicit arguments with clearly defined premises, chains of logic and conclusion. But as far as I've ever been able to make out, these suffer from fairly stark fallacies, and I imagine most theists prefer the informal ones in any case.
It's an interesting project, but worth bearing in mind that the most likely response (possibly after 'evolutionary psychology is just so stories', something which I sympathise with in several cases I've seen) is to come up with similar cognitive arguments for why we're predisposed to believe in natural selection or a godless universe. The classics like 'wanting to do whatever you want' and 'not being able to come to terms with nasty things in the world' will loom large, but it might be worth someone looking at it from a more scientific point of view.
Even if analysing the psychological roots of a belief is seen as only necessary where it can't be explained by the truth of said belief, I think you need to argue for that case and look at why people believe the truth, which isn't always for strictly scientific reasons.
De Cruz & de Smedt (2010) tries to explain, using cognitive science, why many people find design arguments so compelling. Abstract: