I understand your perspective but that's not how I read it, consciousness has several meanings, and I don't remember Jaynes arguing for the one typically used in philosophy of mind (which, like you, is what I'm inclined towards). In fact I mention this right in the second paragraph of the review.

For actual consciousness, in the sense of any experience or sentience in the traditional philosophical sense, as far as I'm concerned, bicamerality is completely irrelevant. Same with self consciousness for that matter. When you say that Jaynes’ fundamental claim was that humans were not ‘conscious’ prior to around 3,000 years ago, I'd say that's correct, but with the term of consciousness in the sense of how we generally think about our human conscious experience (eg not bicameral).

I'm quite interested in philosophy of mind, but I don't see this topic having any relevance to it. If Jayne's hypothesis is right or wrong in that we used to experience Gods with no "ego", nothing changes.