What is Your Approach?

[Locke]

Historical evidence becomes less and less accurate the further you go in the past.

This is not a bad statement, but there is a science to preserving historical evidence, and to verifying if evidence has been preserved properly. For manuscripts, this is known as textual criticism.
While it can be argued theory that the Bible would become less reliable in enough time, we still have enough right now that it is reliable, and that problem has now been circumnavigated by modern technology. If you wish to know more I can give you sources that are more reliable than I, and more credible.

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Others have already addressed this issue, but since it appears(I say "appears" because many before you have feigned interest in order to proselytize) that you honestly are interested in hearing the other side of the debate, I felt I would add my $0.02.

By the wording you have used in the section I have quoted it seems that you share the common misbelief that atheism is the stance that god does not exist, when, in fact, it is the position that the burden of proof that lies with those that claim god does exist has not been met. So, the term "atheist" does not denote the claim that a person makes about the existence of god, merely that it does not accept the claim that god does exist. Some atheists do claim that god does not exist, and those atheists are labeled "gnostic atheists," while that stake no claim are labeled "agnostic atheists." The majority of atheists I have encountered(so what appears to be a majority) are of the agnostic variety.

The big problem I have discovered, however, is that many theists take the agnostic atheist postion as one of intellectual cowardice when it is actually a position of intellectual honesty. They believe that it is an attempt to avoid having to defend any claims when it is actually the position that we don't have enough clear evidence make any claims in the first place. For some reason, many theists think that we must draw a conlcusion on god's existence based on the evidence before us, but these people need to realize that the conclusion drawn by agnostic atheists is that the evidence is insufficient.

In that case an agnostic atheist is exactly the same as an agnostic - you simply added an extra category. As far as division of belief I don't see the point. If you're classsfying Atheist as a social group I guess its necessary, but thats not really helping answer the question. The word 'Atheist' comes from the Greek a- not, and theos- God. It is the belief that there is no God. This isn't complicated stuff..