Although I share much or your disdain of source criticism, we can state pretty definitively The Torah didn't have one author, unless Moses discussed his own death in some sort of prophetic way, and proceeded to ironically boast of his own humbleness. I think it's interesting to note that the Samaritan tradition is that Joshua, not Moses, completed The Torah in roughly 1,200 BC. This actually tracks rather well with the archeological evidence as far as a reasonable time for The Conquest, not to mention the shrine on Mount Gerizim.
Scholarship is literally over the place on Torah final composition. Hezekiah, Josiah, Ezra have all been popular theories, with a relatively new hyper minimalist movement trying to move it all the way to the Helenistic period.
Although I'm willing to at least consider the Hezekiah/Josiah schools of thought, I think anything post exile is completely false. For me, the Samaritan Pentatauch bears extremely strong witness to a much older composition. You basically have to find a point on the timeline when the Isrealites and Judahites would be able to agree to the exact same ancient back story, and nothing post exile really adds up. Post Assyrian conquest is at least plausible, but at the end of the day I think the Judges/United Kingdom period makes the most sense.
Going back to the various fragmentary/supplementary hypothesis, I think it's important for people to know how incredibly pluralistic the theories are. Many people get this incredibly false picture in undergrad that the Documentary Hypothesis is well articulated with something like a consensus backing and this couldn't be further from the truth. There are dozens of various contradictory versions of the DHS, in addition to the Supplementary Hypothesis, The Two Source Hypothesis, and the Fragmentary Hypothesis, all with its cadre of adherents, and none of it has a shred of actual concrete evidence to back it up.
My own personal theory is the very, very long scribal tradition is poorly understood. I think there was a degree of latitude permitted by the scribes to update language to preserve the transimissability of the story. However, when comparing all the various ancient traditions of The Torah, from the SP, MT, LXX, DSS, and even the Beta Isreal Orit, one thing becomes clear. You could change HOW you told the story (language, dialect, ect], but you could not change WHAT story you told.