EDIT: this is a quickly dashed out sketch of thoughts - this needs a lot of elaboration, but I thought it was interesting enough to put out even in an unfinished form in case people have comments. This touches on a couple things mentioned earlier in another post.
Some parts of the church are perhaps rightly skeptical about "modern philosophy", including the modern philosophy of science, so one should attempt to make arguments about evolution in a manner that respects a broad variety of philosophies of science rather than presuming a specific epistemology or, for instance, the correspondence theory of truth. There are certainly some positions that I think Christians are required to take (namely, that real knowledge of the material world is possible), but those are fairly minimal, as are their implications. Though even that one can be dispensed with if, as some do, one points out that we have "fallen" faculties of perception and therefore can't wholly trust them to ever give us knowledge of the material world (but see St Augustine's anti-skeptical argument).
In that case, then, and since the crowd I am most interested in dealing with is the YEC "Rose" crowd whose position implies that there is no death prior to perhaps around 10,000 years ago, we can deal with the "fact" of evolution rather than the "theory" of evolution. That is to say, dealing with the complex of facts that include a 4.5 billion year old earth, hundreds of millions of years of complex multicellular life, and a succession of organisms that slowly look more and more like the plants and animals we have today. But no "theorizing" yet, not even a consideration for, say, methodological naturalism. Somebody constructing a theory - whether it is naturalistic in methodology or not - has this pile of facts to contend with. If we come up with a new theory that is seriously at odds with this set of facts, we're not going to be very happy with that new theory.
The YEC will of course have some objections. First, that the earth is 4.5 billion years old is not a fact, it is a conclusion based on a theory plus some other facts. The facts are the instrument readings and astronomical observations and such that, when plugged into the model, spit out that the earth is approximately 4.5 billion years old. This is certainly a fair objection. Another objection is that we are attempting to apply human reason beyond the "Fall of Man". This is less satisfactory for reasons that will become clearer later in my exposition.
The set of facts, then, that we have is the list of oscilloscope readings, dates of astronomical observations, etc that we have compiled. It is a giant list of facts. Let's call this set of facts Set A. With a rather small set of assumptions, we can then generate a rather minimal theory that gets us to an interpretation of Set A that suggests "the fact of evolution". This answers objection 1: we now have a set of facts and a theory accounting for those facts. The second objection, though is met with the following reply: "Great, provide your own accounting for the facts in Set A." They need not use the same assumptions as above. They just need to provide something that explains the facts as well and do so even if we withhold portions of the facts and then see how well the theory fitted without those facts still explains them. Or generate new facts and see how well those fit. The unfortunate thing here is that, even with the claim that knowledge of the world prior to the Fall is inaccessible to naturalistic methods or human reason absent divine revelation, they can't come up with theories that work as well to explain the facts. They are handwaving them away.
Now, of course, as Orthodox believers, we assent to all the truths that the Orthodox Church teaches. There is then a new strategy: we have a second set of facts, namely, the dogmatic assertions of the Orthodox Church. They say all the holy elders and all the Fathers of the Church taught young earth creationism. My point here, though, is that this is not, it turns out, a fact. It is an interpretation in light of a theory that requires certain assumptions and then into which they insert the facts, just as the 4.5 billion year old earth is not a fact. We can take as the atomic facts, perhaps, the manuscripts we have of Genesis, the writings of the Holy Fathers (and Mothers) of the Church, and the manuscripts of the pronouncements of church synods. And whatever other facts of this type that you may think of. We can call that Set B. The YEC "Rose" crowd, then, notes that, while they do not have a satisfactory model for A, they do have a satisfactory model for B and it is the only acceptable model for B. As such, they do not need to account for set A.
So far, I should not be saying anything controversial. Sure, there are thing to quibble with, like what I mean by "explaining" the facts. However, I hope we can pass over those quibbling details, because what matters here is the big picture about the two different stances. One group says that they have a set of assumptions and theories that gives a consistent explanation of set A. The other group says that they have a set of assumptions and theories that gives a consistent explanation of set B.
Here is my problem: I think the first group, the one that has a reasonable explanation for Set A can have a reasonable enough explanation for Set B - it doesn't catch all of the nuances, but it does not go outside the borders that we cannot go outside of, though it has to admit that many things are still left unknown. Fortunately, the Church itself strongly suggests that these issues of origins are somewhat shrouded in mystery, so that suggests a perfect explanation of B is not really obligatory.
Here is my other problem: the second group has immense difficulties with set A and I don't think the Church warrants sufficient confidence in their assumptions for set B to swallow the difficulties with A. It only really works well if you're going to deny that any knowledge of the physical world by naturalistic means is possible - which is a line of argument that has been used. This is already getting fairly long, so that will have to be part 2.