“The Hindu religion does have a massive diversity of supernatural uber-beings, but they’re all manifestations of the supreme being, Brahman. Historically, this allowed many differing religions to be brought under the umbrella of Hinduism, promoting social cohesion.”
Yes, Brahman is Atman, and 5 Lions make Voltron. Hinduism was merely one example of polytheism. It may have a syncretic tradition that wraps up everything and nothing in a nice pot of curry, but there are many other polytheistic religions that do not, or did not, have anything resembling a unity of the gods.
And India is not a very good example of social cohesion. Lots of sectarian violence over there. Especially the disagreement about whether the prophet and god of Islam is to be subordinate to Brahman.
Tweaking your monotheism so that you can convert various polytheists like the Norse, Germans, Greeks, Celts (etc) is, as you put it, a public relations move, and has no bearing on the truth. Except perhaps to make it clear that you want followers more than you want fidelity. These kinds of moves are what makes for things like the Thirty Years War, and other spasms of violent actions against perceived heretics.
“Starting with polytheism is the wrong end of the wedge in a discussion like this (multiplying unexplained entities unnecessarily)”
Those entities are very specifically described by the believers, and play necessary roles in their understanding of the nature of the universe. The Greeks knew much about the actions and personalities of their gods, and how one should behave with regard to their various temperaments and vanities. Same with Ra, Thor, the Moche Decapitator, Quetzalcoatl, and so on. In fact, there were usually specific people claiming that they were related to these gods, and would be happy to sit you down for several hours while their priests spake forth upon the entire chain of descendants from God X to King Y.
What you have is some people claiming one entity exists, with a body of literature derived from older oral traditions backing it up, and other people claiming that multiple entities exist, with a body of literature derived from oral traditions backing it up. All of them are explained to about the same degree and upon the same types of evidence.
And what you want is to get the monotheists to stop acting like the existence of the universe=the existence of one god, when there is no evidence of that. To borrow from the intelligent design crowd for the nonce, if you found a watch, you would think there was a watchmaker. You would also, however, think there were miners, raw metal smiths and glass makers, fine-tool machiners, merchants, food suppliers, and so on.
Why not assume that creation involved an entire community of gods since there are vastly different known entities? We know that complex human-made things are almost never designed and produced by a single person, so why think the complex variety in the natural world could be produced by one being?
Even if you think the universe was divinely created, there is no reason at all to assume that there was only one divine creator.
And no evidence of a single universe anyway.