I'm thinking the Uchiha tablet was not written by Hagoromo. I mention this because I'm under the impression that Hagoromo's brother is the one who wrote it and he purposely left himself out of this story. Why? Madara comes to the conclusion that the Sage failed in his quest to bring peace to the world. The Sage alone and no one else. Besides a history lesson, the tablet also mentions the secret to obtaining power in ways that can be considered immoral, why would the Sage give such information like that?
Unless he didn't, it's possible the Sage's brother purposely wrote the tablet the way he did in order to instigate this long war that's been feuding on for years even after Ashura's and Indra's deaths. Perhaps he's the one who's manipulating Madara, Madara may not even be aware of such manipulation. Maybe he's the one that helped Madara back at the VOTE. As you said, the Sage seemed to imply that the other half of the Juubi was sealed within his brother. Yet mentions nothing of him afterwards. I think that's because his brother was not someone worth saying good things about at the time. Hell, maybe Infinite Tsukuyomi isn't even a dream world. It could be the revival of the Sage's brother who plans on taking revenge for not being as well-known as his brother or felt betrayed or something along those lines. I think there's a lot more to the Sage's brother than we've been led on to so far
But yeah, it seems Madara genuinely did not know about the existence of the brother, felt like that would have been worthy of mention when talking about the defeat of the Juubi. Obito didn't mention it either when he talked about the Sage beating the Juubi in the 5 Kage arc as well.