Christian quasi-naturalism and the argument from reason

There is an important and key difference between what I might call Christian quasi-naturalism (Van Till style functional integrity, etc.) and naturalism per se, and it is that for naturalism per se the physical is not only closed after creation but also the initial conditions are design-free, while for CQN (the position, I take it, that people like Weekend Fisher are trying to defend, as well as Christian materialists in the philosophy of mind like Nancey Murphy) at least the initial conditions are designed. Now there are a couple of different ways of looking at these initial conditions. We might think, on the one hand, that these not only were designed, but that they show evidence of design (and therefore accept some version of the fine-tuning argument) or we might say that while we believe them to have been designed, we might think that God did it in such a way as not to leave fingerprints that science can discover, and so we might accept the idea that even though we think those initial condition are there by design, it is just as reasonable to suppose that they are what they are as a result of, say, our happening to be in a universe that supports life because all of them really exist, and we happen to be in a life-permitting one and not a life-hostile one (big surprise there). People committed to CQN must believe that the universe as it began is the result of design, the question is whether this can be made evident to science or not. Now it looks like there are some versions of the argument from reason that, if they work, require something more than just a designed beginning. For example, if our knowing necessary truths requires causal interaction with eternal realities, this is going to undermine the causal closure of the physical, since the physical realm is a temporal and not an eternal realm. So if that argument works, it's an argument against CQN as well as naturalism. But do all the arguments require this? Are any of the arguments from reason arguments against naturalism but not against Christian quasi-naturalism?