OK - perhaps my understanding is faulty.
I had understood the theological position to be that we are unable to redeem our own sins through works and repentance because we are all tainted by Original Sin - the act of bringing evil into the world being so overwhelming that it is both inherited by future generations (an immoral concept in itself IMHO) and requires the ultimate 'blood' sacrifice by the Son of God himself to expiate the crime.
That is only one way of thinking of original sin, which didn't really develop until the late fourth century. The Orthodox Church doesn't look at it like that. I think that most Christians believe in "concupiscence", which is an inherited tendency to choose what is wrong, but they do not necessarily believe in inherited guilt, which is what you seem to be talking about. It is, after all, surely absurd to suppose that someone can be culpable for the acts of his or her ancestors.
Also, the language of "blood sacrifice" and "expiation" is only one metaphor that has been applied to the atonement. There are others. In the Orthodox Church, again, salvation has historically been understood not as some ghastly blood-drenched sacrifice to overcome a "mass of damnation", but as God joining himself to his creation to lift it to his own level. On this view, humanity is imperfect - not necessarily all damned by its forefather's sin, but subject to death and corruption - so in the incarnation divinity is joined to humanity and transforms it. Human beings can become immortal and incorruptible, and ultimately become divine themselves.
If you read Romans 6, you'll see that Paul thinks of "sin" not as a burden of guilt that all human beings inherit and which must be expiated, but as an oppressive force that keeps human beings captive. On this view, the atonement is about liberation.
So in short, the Christian tradition has masses of ways of viewing these things. Don't assume that the overly legalistic, Augustinian-Calvinist one which you cite is the only one. That's just one, rather narrow tradition.
So while I agree that we can consider alternative explanations for the existence of sin - as a necessary consequence of free will for instance, or the creation of some unspecified third force - I'm struggling to identify an alternative that warrants, or in fact requires, both the ultimate punishment of eternal damnation and that ultimate sacrifice of Jesus' death.
Again, to view these as an "ultimate punishment of eternal damnation" and an "ultimate sacrifice" are themselves just particular interpretations of theological motifs that can have other interpretations as well. Even if someone believes in eternal damnation, must that be understood as an "ultimate punishment" at all?
And while I agree with the idea that we may all be responsible for our own sins, nevertheless accpording to orthodox Christian thinking a new-born baby has never sinned, but is still damned by its Original Sin - if not then a true innocent would not need redemption, which is contrary both to Jesus' own words and Christian belief.
Augustine thought that, but don't assume that all Christians think that.
Now the argument that you attribute to the fundamentalist is supposed to show, from the basic premises it begins with, that belief in a literal Adam and Eve is essential to Christianity, understood as the belief that God sent Christ to die so that human beings could be saved. As I've indicated, Christianity contains many, many ways of understanding what that means. If you assume just one, very narrow and particular way of understanding it, then yes, perhaps the argument does work. But of course, the purpose of the argument is supposed to be to demonstrate that
all Christians are (or should be) committed to the views it seeks to defend. Evidently it fails in that purpose. It would require a whole lot more argumentation to show that the doctrines mentioned in the early stages of the argument should be interpreted in the ways you suggest.