Mosaic Authorship and the Documentary Hypothesis

Who wrote the Pentateuch (first five books of the Old Testament) and how was it put together? There are two broad categories for the answer.
Traditionally, and still among many evangelicals, it was believed that Moses wrote the entire Pentateuch. Some were willing to give that Moses didn’t write the account of his death, although some have believed that he prophesied even that. Mosaic authorship is rejected by many scholars today.
Many scholars hold to some variation of the Documentary Hypothesis. This theory, in its classic form, states that the Pentateuch as we have it is made up of different documents, of different times, known as J(ahwist), E(lohist), D(euteronomist) and P(riestly). Thus it is often called the JEDP theory.
This hypothesis has gone through many shifts over the years, including the dropping of some documents and the re-dating of others. The point is that many scholars believe that the Pentateuch is a composite text that was written much later than Moses.
Which is true?
Coming from a more conservative background, I took Mosaic authorship for granted. However, I have also studied the Pentateuch and have seen some evidence for the composite nature of it (including but not limited to the names of God). There are signs of editing and Deuteronomy has a different feel from Exodus to Numbers.
What if both theories had an element of truth?
I am not an Old Testament scholar but I would like to put forward a proposal. What if the Pentateuch is a composite text (apart from the five books that are included in it) but that all (or most) of it goes back to Moses?
What if different parts of what Moses taught were kept by different communities within Israel? Some may have been oral traditions and some may have been written fragments. What if at a later time these traditions were compiled, edited and formed into the Pentateuch we now have it?
Is this a slippery slope toward denying inspiration and a high view of Scripture?
Many evangelical New Testament scholars accept something like this when it comes to the Gospels. There seems to be sources for the Gospels and yet they go back to Jesus. You do not have to be a liberal to accept a form of the Two-Source Hypothesis for the Synoptic Problem.
My proposal doesn’t require dating or even counting the sources. It can be as simple as acknowledging that there is evidence of different traditions and of editing within the Pentateuch and that this does not mean that the traditions don’t go back to Moses.
What do you think? How was the Pentateuch put together? Did Moses sit down and write it out pretty much the way we have it or was it more complicated?

