Let's start with what I think is an error in your analysis of polytheism and monotheism: the assumption that both approaches are concerned with ideas about God.
From the outside looking in, it may appear that way. I suspect, though, that throughout history's long course most polytheists have believed their particular god(s) to be quite real. Not the philosophers, perhaps, but the everyday followers. For example, a Norseman making sacrifice to Thor did not think of Thor as an idea but as a red haired, hammer-wielding, belt-wearing god who could provide tangible assistance. Ancient fertility gods attracted worshipers not because they represented the annual renewal of nature but because people thought them real beings who might ensure a harvest or bring about the birth of a child. People did not sacrifice to ideas but to "gods."
Monotheists by and large do not worship an idea of God. They instead believe themselves called to devote themselves to the one living God. The majority throughout history have assumed God to be actively concerned for the creation, the people he has drawn to himself, and for the rest of humanity as well. To varying degrees, they also have believed they need God in order to become what God created them to be.
I think you would suggest that in both cases the gods or God worshiped are constructs of the human mind. My personal position is "yes and no." The living God reveals himself in any number of ways. I think he most fully reveals himself through the story of a particular people with roots deep in Middle East history and through the "ripples" which spread out from that history. We differ on the fundamental question of the nature of God. At the same time, no one can deny our tendency to package God in ways amenable to our cultures, sub-cultures, professional disciplines, or personal tastes. Unfortunately, some of these packages amount to little more than tribalism written large--hence religious wars and persecution.
All of which leads me back to the matter of idols. After all, what is an idol other than a religious package of some sort? The second commandment seems to insist that we take idolatry seriously, that idolatry has short and long lasting consequences. I'll look forward to your take on the matter.