It is not true that just because a person has a prior about what life is — and we all have priors, yourself inclusive — that they will distort the facts just to provide support for their priors.
That some people question the evidence for Saul, David, Solomon does not disprove the evidence, in fact confirms existence of some evidence. Questioning means,
‘yes the evidence exists but I am not sure how much weight to place on it’.
Given you, and I, and historians agree there is some evidence, however, scanty, and given it is the weight as opposed to the credibility of the evidence that is in question, combined all of the evidence leans towards validation of the biblical stories, as opposed to otherwise.
Let me end by asking, would destruction of Judah have been such a significant conquest for Nebuchadnezzar if Judah was small and insignificant and kings of Judah irrelevant? No king boasts of a conquest over an insignificant enemy. Mind you the boast is recorded extra biblically in Babylonian sources.