Your thoughts on Deuteronomy are along the same lines as I have been bringing out on Leviticus. In the
"Jesus wasn't a Sacrifice to Forgive Sins" thread.
IMO Leviticus was written after Deuteronomy. Neither was written in the desert by Moses. I do think that orals stories were passed down through the years, but I don't think they remained unchanged.
I found this site today, which goes along with what we are thinking.
Who Wrote the Bible?
A gentle answer turns away wrath, But a harsh word stirs up anger.