Your approach is a valid scholarly approach, but not one of faith.
David Klinghoffer's book "The Discovery of God" explains the very different approaches. The text of the Torah read without the Oral Law, appears to the secular person to be contradictory. That is because you only have part of the picture.
The Oral Law, which Orthodox Jews of faith believe is part and parcel of the God given Torah from Moses at Sinai, explains that what you see as a lapse of continuity in possession of the Torah (Kings 2/22) is in fact something different.
There was no lapse in custody. In Kings 2/22, the Torah scroll rediscovered after a lapse of some fifty years was not the only one but the original one from Moses at Sinai hidden to protect it from the idolotarous King Menasseh, of that period. During that time copies of the Torah were extant and in use.
Must not have been many copies out and in use!
More recent archaeology says an Egyptian had pretty well shut the place down just a few decades earlier.