Jewish scholarship comes to a conclusion that is somewhat similar to yours.
While sages of the Second Temple era held the book to be a product of the prophet Samuel, today we Jews employ critical methodology that lends to a different view. The book appears to be a patchwork of folklore, legendary tales based likely on historical figures but with little of the history kept intact. Composed likely after the northern kingdom of Israel fell (the late 8th or 7th century B.C.E.), it has a very pro-Davidic stance. It may have originally been a composition or a collection of stories devised to promote the worship of YHVH when the Davidic dynasty adopted it as the state religion and enforced this requisite via a political initiative.
However what we have today has been assembled via heavy and complex redaction, and the later editors have left even less of the history than the original once did, focusing on the religious significance of the folktales instead of offering journalistic reports on a historical tableau.
The Song of Deborah does appear to be older than the rest of the work. It employs an archaic form of Hebrew, and our modern Jewish scholars suggest that the song existed before the narrative that is said to have inspired the song. It may be older even than the song of Exodus 15, used as a template by the Jews of the Babylonian diaspora to flesh out the narrative of the crossing of the Sea of Reeds.
The only real difference from your take is that we Jews hold to the view that YHVH was probably introduced via the Moabite tribes of Sinai instead of the Edomites.