You made the claim that "the metric field need be everywhere ... constant", at least this is as I has interpreted your text, as a consequence of the Ricci tensor being zero. This is wrong for several reasons, and I have given them. If I have misinterpreted this part, sorry, but I see no different interpretation now too. I was unable to understand the point you have made in the remaining text, thus, I'm unable to answer this.
My understanding is that which aligns with what mainstream understands, not your ludicrously ridiculous misinterpretation of isolated text. And going on your claim to have a TOE, that proves you are a poster of untruths.