If you want syllogisms rather than polemic, though I doubt a syllogism will be particularly effective.
(1) The discovery of facts requires interpretation (of information, evidence...).
(2) Interpretation requires narrativisation, emphasising some things over others, selection of relevant detail.
(3) The discovery of facts requires narrativisation, emphasising some things over others and selection of relevant detail. (from 1,2, MP)
From what I understand of your notion of arrangement, an arrangement is a mapping from the collection of all facts to a subset. The mapping will be done in a manner that involves judgements of relevance, questions of emphasis, flow of story etc...
Using that notion of arrangement, you separate accounts from truths:
It is not a flaw, it is an unavoidable consequence of intelligence, that you are able to arrange truths, interpret them and argue the meaning of what you've brought forward is an amazing thing. And it cannot be contested by truth alone. — Judaka
I do not contest the claim that some conflicts cannot be contested by truth alone; some people disagree on right and wrong. What I contest is how you are using the notion of arrangement to separate truths from stories using them, based on the argument above. An arrangement is not a mapping from facts alone to interpretations, it's a productive relationship from facts and interpretations to facts and interpretations; you need to interpret+investigate skillfully to speak truthfully and keep falsehood + irrelevance at bay. The facts alone don't do that, you gotta put their interpretations (and their contexts + stories...) in the mix to do anything with them - to link them up and reason and investigate.
And since the facts alone don't do that, and even basic truths require that structure, the resultant picture assuming your framing of "arrangement" is an unduly skeptical one. It demolishes the connection between facts and accounts generating them at the same time as emphasising that all we ever make are accounts (the irremovable subjective element)... So there's no contact between us and the facts wherever it matters.
I am with you that facts under-determine interpretations; I am not with you that the under-determination of interpretations by facts allows you to conclude that (unspecified commonplace things) cannot be decided by facts - because there are judgements of relevance, emphasis and narrativisation that go into the facts themselves through their discovery mechanisms. If you think about facts in a manner that does not separate them from interpretation (hence all this talk about facts guiding interpretation previously...), then it addresses this global underdetermination = cannot be contested using facts thesis. The facts come with interpretations, that makes some facts weigh heavily on some interpretations (eg: refuting them, rendering them implausible...). Relationships between facts and their evidence should be brought out in an account using them; there is a structural symmetry in the domain of the map (facts) and the image of the map (selected subsets) that the notion of an arrangement as you were using it does not portray. The structural symmetry being evidentiary relationships among facts, what interpretations they engender and so on... showing up as lending support in an account through those relationships.
The purpose of all the polemic was to portray you as someone who purports to be using "just the facts", but is actually taking a lot of liberties with storytelling. It was intended to use the same idea as in the argument above. I took to posting in that style because it is extremely difficult to convince someone who believes in "just the facts" about anything, regardless of whether they are wrong. Because, you know, they allegedly just believe facts. In my experience, those who emphasize at length about facts in discourse are usually doing so to support their own worldview; it's a backhanded criticism against all that they do not believe. It purports to be an injunction to reason, but it actually functions as a means of rendering ideas invulnerable to critique. Reason as insulator. If you one day decide to waste an evening watching Flat Earthers on Youtube, look out for how much they emphasise the scientific method, skepticism, and conservative interpretation of evidence. I am not kidding you, they really say those things a lot. It's very easy to take on the posture of a rationalist without actually being one.