What's more, it would be foolish to overlook the tendentious nature of many of these texts. Mostly, they're hardly neutral, are they?

True. Then again as CS Lewis pointed out, all of the contemporary accounts about Napoleon were written either by the French, who idolized him, or by the English/Germans/etc., who despised him. There are no neutral sources. From this we do not conclude, however, that we don't know anything about Napoleon.

Of course a flaw in this analogy is that we don't have many contrary sources about Christ. Mostly we have the canonical NT writings, a bunch of gnostic texts, and a reference in Josephus which appears to have been garbled or mangled (or just straightforward embellished) in the process of being handed down.

But really the problem is that you have defined all of the types of evidence that Christians have for their religion as out of court, mostly because the only evidence you accept as in court is scientific evidence. At which point all I can do is throw up my hands and admit, no, we don't have any scientific evidence for the existence of God. But, as I said, it's not a scientific question.

I mentioned above that the type of evidence that most Christians have for their faith/belief breaks down into (a) historical documents, (b) testimony of trusted persons, and (c) personal experience of the divine. The problem is that when anybody presents any of this evidence, they are pounced on because it's "not conclusive" or "not rigorous and repeatable" or what have you. Well, yes. It's not a scientific question. It's a matter of looking at the existing evidence, and deciding if one finds it convincing or not. It's not a mathematical proof or scientific validation. It is, as some of the more calm and reasonable people on both sides of the fence have stated, something about which good and rational people can go either way on.

The ugliness starts when either side starts flinging poo at the other. The religious side tends to fling (a) eternal damnation, and (b) accusations of immorality; whereas the areligious side tends to fling (c) accusations of irrationality and stupidity. Leaving (a) aside for the moment, neither (b) nor (c) are really fair.