What we need is to define God. It is possible that I could define God in a manner which makes (vii) and (viii) factual. For example if I define God as David Attenborough, then sentence (vii) can be independently checked and found true making (viii) false. However this kind of definition is not what we usually mean by God. Rather by God we mean something which in classical theism is transcendent. Everything else which exists does so imminently; that is they exist within the universe and we can interact with them. God, as defined in classical theism, exists transcendentally, and so is neither within the universe, nor can be interacted with in the manner of other objects.
This issue of defining "god" is always the sticky bit. I'm not sure exactly what you mean by "classical theism," as there are significant differences between different versions of traditional theism. That is, the Hellenistic monotheism of Pythagoras and Plato is not identical with Judaic theism, neither of them is identical with traditional Christian theism, and all differ in various ways from Islamic theism, even though all have at least some elements in common with one another.
In the case of the Abrahamic theisms, all claim that "god" has intervened in human affairs in various ways, causing "miracles" and communicating through humans (prophets, etc.) to humans, said self-revelations of "God" being preserved in certain books. "God" is said to be not only transcendent, but also immanent ("omnipresent") in the created Cosmos. In the case of (non-Gnostic) Christianity, "God" is said to have directly incarnated himself in human flesh in the person of Jesus Christ. The Abrahamic monotheisms make testable claims: Yahweh unleashed devastating plagues on Egypt as recounted in the Exodus story--or not. Yahweh resurrected Jesus from the dead in the midst of various extremely public cosmological displays of power (a great earthquake, darkness upon the land, a resurrection of dead "saints" who went into Jerusalem)--or not. Etc.
Nor am I sure that the Hellenistic monotheists would agree with your argument. Plato's famous allegory of the Cave relies on the premise that the transcendent realities are made imperfectly manifest by the appearance of their shadows on the cave wall. For the Pythagoreans, the nature of the Divine was revealed in the nature of Number as manifested in mathematics, geometry, and the study of vibrational tone. For the Gnostics, their transcendent "God," though wholly detached from matter, could be experienced in the state of gnosis. So, I'm not sure that any of the traditional variations of monotheism would agree that their "god" fit entirely and solely within your "poetic" category.
This means that God, so defined, is not merely beyond independent checking on practical grounds (like our teapot orbiting Pluto); but in fact necessarily beyond checking. This is worth re-iterating. As defined in the manner of classical theism, God's existence is, by definition, impossible to independently check.
Any proposed god (or entity of any other sort), the existence of which is indistinguishable from its non-existence, even in principle
(as you're arguing here) is, for all practical intents and purposes non-existent. Occam's razor dispenses with any solely "poetic" gods. As Anfauglir points out, theists would dispense with them as well. A "poetic"-only god cannot receive worship, hear prayers, provide hereafters, offer commandments, "inspire" books, or any of the rest of it.
If we accept this definition of God then we must conclude that sentences (vii) and (viii) are poetic.
I don't think this follows. Your argument assumes that there are only two possible kinds of statements: "factual" (statements about real things) and "poetic" (statements whose meaning and "truth" are purely subjective). A theist could argue that there is a category of "spiritual" statements to which their understanding of god-talk belongs, and that the truth of "spiritual" things is apprehended via direct mystical experience of "spirit." It is arguably possible to talk about "mathematical" statements. For example, "It is impossible to calculate all of the digits of pi." As far as we can tell, this seems to be the case; yet, the Cosmos does not have to accomplish the impossibility of calculating an infinite number of digits before it can produce a soap bubble.
Also, your statements "anger is red" and "anger is not red" are incomplete as written. The first implicitly assumes some particular person's nervous system and/or "poetic" metaphorical construct. For example, "Anger is red [in this cartoon I'm drawing where the angry character's face turns red and steam comes out of his ears, because I'm analogizing anger to heat and to the reddening of the face of an angry person]." The latter statement is either straightforward ("Anger is not red [because it's an emotion silly, and it doesn't emit or reflect red light]") or differently poetic ("Anger is not red [because we sapient cephalopods from Tau Ceti turn blue when we get angry"]).
The reason "Anger is red" and "Anger is not red" do not contradict each other (as you're using the statements here) is because the implicit portions (which specify whose neural structures and/or metaphorical constructs are defining anger as red or not-red) are not the same in both statements. IOW, "anger" is not "red" and "not-red" at the same time and in the same respect--because the implicit portions you've left out differ from one another.
So, you have not created some separate category of statements that exist in a permanent Schrodinger-state of "true/not-true" in some "transcendent" or "poetic" realm forever safe from any kind of fact-checking. The use of E-Prime (English, but without any of the forms of "is") is a handy way to clear this up. Instead of "Anger is red," E-Prime flushes out the hidden component: "My mind analogically models anger as red." Instead of "Anger is not red," we get: "My mental conception of 'anger' does not include a color; I view it as an intangible emotion" or "My mind analogically models anger as blue, not red, because on Tau Ceti IV, we turn blue when we get angry." Once you include the poet in the "poetic" statements, they become subject to fact-checking. A given person "poetically" considers anger "red" at a given time, or they do not.
This means that neither (vii) nor (viii) are factual statements and so do not share any mutual dependency. This leads us to a strange conclusion. The sentence “God both does and does not exist” is not a contradiction!
To "exist" is to be part of reality. Poetic statements, metaphors, similes, analogies, etc. exist as products and procedures of human consciousness. We can say "Shakespeare's sonnets exist" even though they are poetic statements. We can even verify this by going to the library or Googling them. In the same way, we can say "Darth Vader exists"--as a character in a set of stories. We can also say that "Darth Vader does not exist"--as a real man with magical Force powers. The two statements do not contradict one another because of what comes after the dashes.
In like manner, we can say "God exists"--as a memetic construct that many people believe in and worship. We can also say "God does not exist"--as a real, omnimax super-spirit of the Cosmos outside of human minds. However the statement "God both does and does not exist" as you're using it here is a bit of a semantic shell-game, because the "exist" and "does not exist" clauses are meant in different respects, so the validity of "both" as a connecting term is dubious at best. "The San Francisco 49'ers are and are not Super Bowl Champions." This is true, but dodgy, and it does not mean we need to be "ignostic" about the San Francisco 49'ers. The aces up the sleeve are the unstated parts: they "are" Super Bowl Champions because they've won Super Bowls in the past. They "are not" Super Bowl Champions because they lost this time around. No one would suggest that it's impossible to fact-check and find out if the 49'ers won the Super Bowl or not.
Sentences about God's existence, both for and against, are in fact poetic statements which tell us about the speaker rather than the world the speaker inhabits.
I do not see a legitimate dichotomy here. "The speaker" is an inextricable part of the world (reality). If "the speaker" believes that "god" exists, this belief will have certain effects, even if it's only to cause the speaker to say "Yes" when asked if they believe in "god." It might well cause them to vote Republican, or throw acid in the face of a little girl because she's going to school. Or, it could motivate them to work tirelessly to aid the poor. In other words, the state of "the speaker's" consciousness with regard to "god" (believing, or not believing) is itself an element of "the world" (reality).
If you try to distinguish
"god" from "the speaker"--that is, examine the question of whether or not "god" exists independent of human minds like "the speaker's"--then "god's" existence is a factual question again. If "the speaker" tries to argue that their "god" is "poetic" only, and cannot be found anywhere outside "the speaker's" poetry, then they're admitting that their "god" does not exist
--as a separate, independent, real agent. It is this latter sense of "existence" that atheism is concerned with. To say that "god" is "poetic" (as you're employing that category here) is to agree that it does not exist
as a real Being. Which is to agree that atheism is correct.