When Jewish scribes made copies of the Torah and the Tenach, they counted the value of each letter that was in the original scriptures, and when they finished copying the new one, they would count the value of each letter they copied, and if the totals didn't match, they DESTROYED IT, and started all over again. That is how they were able to keep the scriptures free of errors. It was God's plan that an incorrupted Bible be passed down from generation to generation because it was HIS RECIPE FOR LIFE, and He would NOT allow it to be corrupted as you have so blatantly manage to accomplish.
A small section at the beginning is, in fact, taken directly from Kings II, just shortly BEFORE King Josiah.
Most of the rest of the book concerns matters far later than Josiah. Ergo, this very oldest material is still post Josiah.
Maybe someday someone will find something older.