I point out, for illustration, the theory of dark matter/energy and string theory. Both of which have started out as hypothesis with few if any testable ways to observe them. At a Google tech talk Murray Gell-Mann, whose lab was where the idea of string theory arose, indicated that he was not very impressed with the idea and suggested it was completely untestable.

The challenge I see in God theory is that it is that people go off and start from some concept they learned in primary school and poke holes in that image. Rather than actually taking a scientific approach and asking what the nature of God might be, given the data they do have access to.

Note that this is completely distinct from theology, or the study of religions, rather it is an attempt at understanding God (which is often referred to as enlightenment).

As Dawkins and others have pointed out however, the God 'meme' has been used forever in human cultures to assert power over one group by another. Thus there is a lot of mental baggage around taking God seriously (think confirmational bias on steroids).

Example, I once talked to an engineer who would not even posit the existence of 'a' God because for them it meant there was a hell and they were afraid to think about what it would mean to spend eternity in such a place.

From that example you can see the confluence of what they were taught by a religion as a control mechanism (obey us or go to hell) versus his ability to ask critical questions.
I suggested that a 'God' might exist and their might not be a hell. He found that pretty heretical but it gave him a way to ask the question without wincing.

My wonderings are around the source of sentience and the implementation of free will. Generally the debates of philosophers rather than scientists but one in which the presence of a 'God' (in the scientific sense) could be hypothsized as the difference between sentient and non-sentient. I thought it would be fun to write a short story where confirmational bias was the result of God knowing what you wanted the outcome of your experiment to be and making it so, leading too a lot of angels in therapy because they had made it work like you wanted and then you were all irritated that it wasn't reproducible or something.

Your approach could be used:

Now, God theories in general have multiple issues that make them unscientific. For example, if you claim that God is an entity that is 'beyond time', you need to define in scientific terms what it means to be beyond time.

Ok, so we'll put this 'God' entity thing in a dimension that is orthogonal to time like one of the 11 in string theory.

Another issue is that you would need to come up with some experiment that would prove that God does not exist.

You do have to work on some experiments, and being falsifiable is a slam dunk, but given that we're talking about something that has a will (or is will) its hard. I've often suggested that I can read the phone book for Perth Austrailia and see an indication that a Tom Smith exists, but if I can't get to Austrailia or contact it in anyway I'm hard pressed to prove he exists, even though he has a home address and everything. This is the current challenge with Dark Enery/Matter as well which is coming up with ways to actually see it. And we can't so we look for ways it would influence the stuff we can see. You can make the same argument for God, look for ways that if God exists things might be different. (caveat confirmational bias etc etc).

Even if you were to formulate a definition of God that would satisfy these requirements, it is doubtful that many believers would agree with that definition.

There is no rule that says for a theory to be legitimate it has to be believed by everyone :-) Many solid theories started out being believed by no one but the theorist themselves.

Thus, 'God theory' in general doesn't describe a scientific theory at all, and so it is fundamentally not related to science.

I don't think you succeed in your claim that God theories are 'unscientific'. I would agree with the claim if you said that some theories put forth about the nature of God are unscientific but that does not preclude the existence of a scientific theory about the nature of God.

To have a theory about God, you have to first accept, for the sake of argument, that God might exist. Then you can start looking ways to put boundaries around what God might or might not be, sort of like how collision analysis of partcles is telling us where the Higgs boson isn't. I caution you though, if you start looking for God you run the very real risk of being found.