There are books answering these contradictions because there are just as many making the claims that they exist. Surely the existence of answers can't be construed as some sort of evidence that the answers are shaky or unreasonably "creative". And you're right, it's a false dichotomy, but the simple fact is that we don't assume two authors came to completely different conclusions about a fact that they were apparently both witnesses to. That would suggest there was something seriously wrong with one of their accounts, but if we're going to make that conclusion, the burden of proof is on the person who says there was something wrong with their accounts rather than the ones who say context is important and an apparent contradiction can probably be explained by something other than any mistake at all, never mind an "honest" one. You can't just pull two seemingly opposing statements out of a text and assume they're some sort of mistake. You first have to look at the context, and that's what all of these "libraries" of defenses against the supposed contradictions are doing. They're pointing out context that the many skeptics readily leave out because they have no interest in the context. They're just looking for mistakes and not being objective, so yeah, it takes a lot of work to respond to people who cause undue doubt about the congruence of the Biblical narrative by carelessly searching out anything that seems a little strange to them and automatically labeling it a "contradiction."
You're attributing a standard to me that I never gave, which is a straw man argument. OF COURSE I am talking about reasonable explanations, not ridiculous ones. All we have to do is point out one possible explanation that fits all the facts and doesn't generate more questions than it answers. The burden of proof is on you that we can't do that. You have to prove, first, that there is no reasonable explanation for the facts in the narrative. For every "contradiction" offered, there are usually multiple REASONABLE theories that make the two statements compatible. You have to prove that all of those explanations fail in order to establish that an actual contradiction is the most reasonable explanation.
Yes, it is, and I think you're wrong about that, too, but more to the point, the burden of proof lies solely on you, the skeptic, to prove that there's a contradiction. This is the way it's done in evaluating historical texts. You can't give equal weight to the "mistake" theory as you do to the "there must be an explanation" theory. Historians always look for an explanation before chalking it up to some kind of "mistake" because investigating why the two claims were made may open up opportunities for further discovery.
So before you tell Christians that they are just coming up with creative excuses to avoid a problem, you need to question whether there was actually a problem in the first place. As with all ancient texts, you need to prove that one of the accounts can't be trusted, and if you fail to prove it, then the accounts in the Bible come out just as unscathed as before you showed up.