What are your criteria for determining that the text is "inspired"?
You are asking the wrong question. "your [or my] criteria" are irrelevant, as I keep saying. God already told us in the word. God always get to define. Yet, you have a man-centered view, and I do not. The Bible says:
2Ti_3:16 All scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness:
Therefore, the question moves to, "How do I know what is scripture?" Simple, God told us in it, but that is another question and another study.
How do you know that the KJV and the TR are "preserved" as the accurate historical text available today?
I never said anything about 'the TR' (there are several variants). I am not a 'TR' person. I am one who believes what scripture says, in that God "inspired" and "preserved" His word to this present moment, and have His word in my hands and can hold it (KJB), and show it to all for them to see it.
To be a 'TR' person, is close to truth, but not the complete truth, but is more of a 'hedge'. I do not say that the 'TR' (as was consulted for the AV) is not of value. It is, but not in the way others who are 'man-centered' see/understand it.
God already stated that God would "preserve" His words, and I believe that promise:
Psa 12:6 The words of the LORD are pure words: as silver tried in a furnace of earth, purified seven times.
Psa 12:7 Thou shalt keep them, O LORD, thou shalt preserve them from this generation for ever.
among other texts, and God cannot lie, in that two things, [1] God cannot lie, and [2] God promised, based upon His own name/character to so fulfill His word, which never returns to Him void (empty of fulfillment), for it always bears fruit.