I have to register a note of disagreement here. Mainly, because many of the heroes of the faith who were in government, served in pagan states which certainly were not Jewish theocracies. Joseph was prime minister of Egypt, Daniel served the Babylonians, Queen Esther was queen of Persia. And in serving these ungodly governments is where they had the best influence. (In fact the kings of the Israelite theocracy were mostly a bunch of backsliding screwba'als by comparison!)
This pattern continues after Christ. I could cite a lot of examples, but one will suffice: William Wilberforce, the devout Christian parlimentarian in Britain. His contribution to history: leading the charge to outlaw slavery in the British Empire. Surely such a man would have merited mention in the Scripture if he had done his work before the time that it was written.
So I'm convinced that God cares intensely about government. I just don't see the "clear as a bell" shift that you claim you see.
Of course, government is certainly not His FIRST priority, but, that doesn't mean it has dropped off his list.
Won't we end up just picking those figures which reflect the view of NT we already had before we started picking?
No, the text of the Gospels is what we have. And what we have there is a personality who is CLEARLY different in style and focus from the OT figures you cite. Joseph, Esther, Daniel -- none of them would have said "My kingdom is not of this world". But Jesus did, and you expect Him to change this like He changed everything He commented on, because of Who He Is.
If we don't use the gospel texts to form an attitude to politics, can we just hew the prophets of Baal with the sword (like the prophet did) and be done with it? Why not? He was a "hero of the faith", wasn't he?