They make a clear distinction between the divine power and the intercession of the saints who pray to God on someone's behalf. Seeking the intercession of the saints is seen as the same as asking a friend to pray for them.
Is it really, though? Take the Virgin Mary, for example. There are, at least in Catholicism, specific, formulaic prayers to Mary. She is believed to be an entity with...supernatural qualities capable of intervening in the world in a way that ordinary humans are not, even if via appeal to a higher divinity. The same is, as I understand it, true for the Saints to some degree. Also, there is reason to believe that many saints are--how shall I phrase this?--in part reskins of traditional polytheistic gods or heroes.
This is simply not the case. There are countless non-Christian scholars of Christianity that understand the doctrine. The supposed logical inconsistency below fails to address Trinitarianism at a most basic level.
Oh, I understand what the Trinity is defined as, certainly. I just think it is logically inconsistent, and only becomes believeable as opposed to understandable via a leap of faith. Everything is a continuum--on the one hand, there are beliefs that are easy to empirically verify, i.e. that things fall when you drop them. Then you have things like the existence of a God, which is not as easily shown but which even most atheists would admit *could* exist, logically speaking, even if they find it highly unlikely. Finally, you have the Trinity, which becomes logically consistent by the leap of faith in not only a god, but a god which can...bend the laws of logic--i.e. it becomes believable not by empiricism, but by the act of believing it, at least as far as I can wrap my head around it.
That being said, I am always puzzled when I hear someone expect a comete logical consistency in a description of a classical monotheistic God. It seems the height of human arrogance to expect a being with the characteristics ascribed to such a Being to fit into human-made boxes like logic.
If I'm going to be analyzing something logically in a discipline like history, then I need to define it in such a way that I can use it logically, particularly to answer a comparative question like the one posed in like terms. Am I saying that it's perfect theology, or theology at all? Of course not. It's a different approach. Anthropology of Religion, perhaps, would be the overly-dignified term.
The analysis provided above is not an analysis of Trinitarian theology.
Analysing actual Trinitarianism as polytheism in any way immediately leads to the conclusion that it is not polytheistic.
Of course it's not, as I've already said. Rather, it's an analysis of Trinitarian performance, the rituals and practices of Trinitarian Christians, using a definition of Trinitarianism that is theologically imperfect, but, as I can understand it, necessary to make a logical comparison of beliefs between Christianity and various polytheisms logically. If you can point me to a better resource that doesn't at some point run into the identity problem (the equals signs were mathematical statements of the transitive property) please do so either by post or chat. I'm more than happy to learn, I just have yet to see any definition that doesn't rely on belief to overcome the problem.
This is not even a stawman. Maybe a bale of hay with a smiley face drawn on it.
First, that is not remotely the definition of deity as Abrahamics use the word. To them, true Deity involves an eternal, transcendent self-existence outside of creation. No one ascribes that till the saints.
Second, Catholics and Orthodox (acknowledging that not everyone can be accounted for) do not teach that the saints 'draw on divine power to answer prayers'. Rather, the saints are asked to pray on the believers' behalf. This is theologically the same as asking a friend to pray on ones' behalf. There is a difference in expectation: it is believed that the saints, having been filled with God's grace, will more closely pray in accordance with God's will.
What we have here is something that neither walks like a duck nor quacks like a duck
No, but it's a pretty generic descriptor of the line between a mortal and a god in polytheistic belief systems. The OP asked us to come up with a religion, thus I have asked the question, "is x polytheistic" and used a definition of "god" based on what polytheists used/use. If you define a God as "an eternal, transcendent self-existence outside of creation", an argument can be made that Brahman, the Hellenic Logos, or the Roman Numen would be a God, and thus that Hinduism, Greek Polytheism, and Roman Religion would all be monotheistic. But, for the most part, that isn't done. The exception, attempts to fit Hinduism into the category of monotheism, relies on taking a Hindu concept and mapping it onto Abrahamic monotheist ideas about God--and, in a certain sense, it can. It really isn't any different to question if Christian concepts can be mapped onto Polytheistic conceptions of God.
And as for the comparison to asking a friend to pray for you, here's where the point I made prior comes into play. It all hinges on whether you define monotheism vs. polytheism for the OP's purposes based on theology or based on the performance of faith in daily life, i.e. on the manner of ritual, forms of prayer, etc. as well as the genealogy thereof. The Virgin Mary has specific, formulaic prayers; many other saints--or saints as a body--have specific rituals. Theologically, a prayer to Quetzalcoatl, a prayer to Ganesha, and a prayer to the Virgin Mary are worlds apart--but practically, we might call all three approaches polytheism, because of the ritual similarity in the construction of and prayer to separate supernatural entities overseeing certain spheres.
And as for the point about art, the fact remains that, in Christian art, there can be found depictions of God the Father, Christ the Son, and the Holy Spirit with separate attributes and with separate forms. They may be depicted all together, or separately (as is the case of, say, the famous section of the Sistine Chapel roof). They may be conceived of as the same being, but they are portrayed as separate beings. In other words, the theology is monotheistic, but the performance--the depiction--is polytheistic. Really, it's a similar question of emphasis as in the Hinduism question.