Celsus

An alternative to spin's explanation is that Ben Sira had not read Kings, or that he did not consider others like Solomon, Jehu, or Jehoiachin to be good kings. Whether these are "easiest" explanations or not, it's rarely the case that history is so simple, and we all know about problems with Occam's razor. The LXX was being written shortly after this, and it's hard to see Kings being invented and then translated so shortly after and being regarded as a holy book in the tradition of the people of the Book.
Well actually, their "accurate" locations rarely go back more than a few centuries, and are not necessarily based on contemporaneous memory. The example of Biblical Ai is a case in point (that everyone but the evangelicals will agree on): It is clearly written as a historical narrative, but clearly fictional since Ai was a mound of sand and dust at any point during the Israelite's so-called conquest. Maximalists forget that although many passages are written "historically", we cannot ascribe any confidence to their historicity until proven by external evidence. On the other hand, the Biblical location of Ai is probably right on the mark. Does it "recall" actual events that led to the destruction of Ai? Hardly--the destruction on a second attempt has clearly theological value in the story-telling, no matter how "unlikely" apologists may argue that telling stories of defeat are (if in an exilic or post-exilic period, emphasising defeat because of ritual impurity would actually be a likely scenario). Worse yet are the apologist (Glen Miller, specifically) attempts to claim 300 people at Ai fought off 30,000 Israelites.

All this just goes to show that no matter how "historical" a written record may seem to us, or unlikely the extenuating circumstances, or how humiliating to the writers and people, it is no basis on which to claim it must have happened, or even has underlying historicity. To do so is to practice anachronistic reading, fitting our own mentalities into that of the writers.
Well the Mesha stele is quite controversial, whether it reads "House of David" is hardly conclusive. Secondly, names do pass through history amazingly well--Ugaritic tablets all show early records for Canaanite deities like El, Asherah, Baal, Anat, etc., but their versions are distinct from later Canaanite ones, or the Phoenician Baal (Ahab and Jezebel's?), or the later Israelite syncretic El/YHWH beliefs. Judges and Samuel shows some evidence of older myths being written to cover up the older myths--Jerrubaal/Gideon being the prime example, in which Jerrubaal "May Baal contend" is apologetically explained in a bad way. Meribaal and Ishbaal in Samuel are changed to Meribosheth and Ishbosheth, replacing "Baal" with "Bosheth" or shame--something we only see much later in the book of Jeremiah. So names are resistant to change, place-names as well, since many of the places (Gaza, notably) retain their names even into modern times. You have to remember that Israel was not very large (certainly smaller than England), and the local geography would be well-known by inhabitants, and resistant to change (since they rely on intersubjective agreement, to facilitate directions, trade routes, and the like).
If the house exists today, it existed at any point in which the later biblical writers existed (we have no idea how much sand covered it though). Certain legends do pass on well, others do not. Solomon's greatly exaggerated temple is also well-attested to with comparable design of temples in the Iron I, but there was never a single one, and they were all over the place. Architecture is also likewise subjective in its interpretation: Solomonic gates are disputed by Finkelstein as being Omride, for example.
How about the traditions of the people who stayed in Palestine vs. the traditions of those who returned from exile (i.e. early Samaritans vs. Judahites)? What about different tribal school traditions whose histories began to diverge with sufficient insularity? If, like Van Seters, you see D as the first source, J as the second, and P as the last, this is not a problem at all: Josiah's lot write D while Judah is the only one standing. J emerges on return from the exile, where man pre-J elements and J itself are supplemented to D, and then P, possibly associated with Ezra becomes the final supplement and superstructure incorporating both the previous two. The problem with traditional Documentarians is that they assume that just because someone gives precedence to "northern" towns or tribes, that person must have come from the original Israel. Why not from a later period? (I believe spin can make this point much better than me)
I would see D as exilic (at the earliest, contra Van Seters), J(E) as post-exilic, and P last of all. Just because Judah existed prior to its capture (and probably around the time of Israel's demise) does not mean it started writing down its records. Perhaps king-lists, trade documents, and the like, but cultic practices were diverse over this period, and I disagree that Josiah's reform is possible because I do not think it was centralised enough, or powerful enough, to institute monolatory that early on. It is only (to me) the period of the exile in which the priestly remnants could have started the revisionist work of writing out all other Judahite traditions (or subsuming traditions about El, Asherah, Baal, etc. into Yahwism). On return to Israel, the picture changes again, and J adds on to D recognising that the picture is too simplistic and falls short of giving Israel a long enough history (E cannot be confidently identified, aside from its use of "Elohim"--clearly, its regional focus seems to be not in the Northern Kingdom, but around Negev and Beersheba, and there are passages beyond which that no one can agree upon. E, if specified as above, has no structural or thematic unity, and is therefore more likely multiple sources, and we should speak of E no longer). Much later, P comes in with historiographical ideas borrowed from Herodotus, Hesiod, and the Greeks (with transfer and exposure made possible circa. Alexander the Great's invasion) to give it its final superstructure. That's my current pet theory, probably too simplified, and probably far too naive on many parts, but it gives me a framework in which to think about history in the Hebrew Bible.

RE: Sennacherib:

I haven't looked at this in depth, but I recall the Bible's fanciful version of events showing clear evidence of gloss. Not that I trust either source for an accurate picture, but it does show how easily myths accrue to historical texts. On the other hand, IIRC Sennacherib's inscriptions about Israel were in his reception room for all visitors in order to praise his own greatness. So while a bit far-fetched, it's even possible that the exiles borrowed from the etchings there, and proclaimed brotherhood with the now-disappeared Israel in order to claim much more land on return (when the Persians let them). All of which I thought up in the last 5 minutes.
My point with all my little flights of fantasy is simple: there are a hundred and one possible explanations, such is the nature of historical evidence being so radically underdetermined. To confidently proclaim evidence of J in 9th century Judah, which barely existed, or E in 8th century Israel, which had no monolatric tradition (that I'm aware of), or P with Hezekiah, or D with Josiah, are all problematic, and assume far more historicity to the Bible than is warranted. On the other hand, I do not agree that what cannot be conclusively shown to be early must therefore be late. There are several poems in the Bible that are extremely complicated and the theophoric names are indeed complex. My favourite example is Deuteronomy 32:8-9 in which YHWH is a minor deity under El Elyon (and when Elyon derived from El is also difficult to tell). More radical is Vawter's interpretation of Genesis 49:24-26 (modern translations covering the deities invoked):

• His bow stayed taut,
  His hands were agile,
  By the Bull of Jacob (abir ya'aqob),
  By the strength of the Shepherd, the Stone of Israel, (ro'eh 'eben yisrael)
  By El, your Father, who helps you. (el 'abika weya'zerekka)
  By Shadday who blesses you (sadday wibarekekka)
  With the blessings of Heavens, from above, (samayim me'al)
  The blessings of the Deep, crouching below. (tehom robeset tahat)
  The blessings of Breasts-and-Womb, (sadayim waraham)
  The blessings of your Father, Hero and Almighty, (abika gibbor wa'al)
  The blessings of the Eternal Mountains,
  The blessings of the Everlasting Hills,
  May be on the head of Joseph,
  On the crown of the chosen of his brothers.

In this, "Father" and "Shadday" commonly refer elsewhere to El or YHWH, but Breasts-and-Womb is probably Asherah or Anat (or similar), whom rhm refers to in Ugaritic texts and are commonly paired with El. So while this poem cannot be conclusively dated early, it is almost certainly early, with some redactional gloss (or a later writer who did not understand early Israelite beliefs). Of course, there are few historical portions of the Pentateuch and Deuteronomistic History in which the same can be said likewise, and guessing at which is usually just conjecture.

On the other hand, the clearest sign that J is exilic at the earliest is that the patriarchs are hardly alluded to anywhere in the prophetic books. "Fathers" (abot) is too vague, Jeremiah's mention of the covenant (11:3-4, 31:32, 34:13) is the work of a later editor, and presumes the exilic period (or more probably the post-exilic). Jacob is by far the most commonly cited patriarch among the prophetic works, less commonly Isaac and Joseph. The earliest mention of Abraham outside the Pentateuch is Ezekiel 33:24, which is exilic. Sarah gets her one non-pentateuchal reference in Isaiah 51:2. To then claim that J and E represent seperate, well-known, pre-exilic traditions about the patriarchs can scarcely be taken seriously (by me).

Joel

Edited to ask: does this count as something of a rebuttal to Friedman, as Doctor X challenges at the top of the page?