Thank you for sharing your position in such a clear, non-combative, and well-reasoned way. By your definition, which is a fair one, I would be an agnostic. However, I would choose, for clarity's sake, to call myself an atheist - and here is why.
You define an 'agnostic' as someone who holds no opinion on the divine. While this differs with the common dictionary definition, I believe it is a good definition in its own right. Yet, your position seems to be one where you seem to prefer to be accepting of those who profess a religion. Personally, I see this as an opinion on the divine in and of itself - the opinion that it is reasonable for someone other than yourself to hold a belief in the divine.
In a hypothetical world, let's say there are those who believe that their world is supported on the back of a turtle, those who believe that can be no cosmic turtle, and those who profess that it is impossible to know either way. Let's say that the inhabitants have in fact no way of obtaining evidence for or against the existence of anything beyond their planet's atmosphere. Those who say that it is impossible to know are in fact correct, but there is really no reason for them to respect the opinions of members the other two schools of thought! That would be tantamount to neither agreeing nor disagreeing when presented with an argument that had no evidence or basis. A reasonable person would disagree! If this were not the case, we would be smiling and nodding at every person who made an unwarranted argument.
You may ask, "What is the harm in being non-judgmental when presented with an unwarranted argument or claim?" Well, I propose that in the extreme case, you'd end up having to agree that any given claim was at least possible. "Four-leaf clovers bring me luck" - might be true! This is pretty much unfalsifiable. "Twinkies double your odds of getting cancer." - You'd have to give this claim credence, until someone funded a double-blind study - which probably won't ever happen. Et-cetera, et-cetera.
Sorry for my rambling argument - but I hope you can catch my drift. What I want to say is that, just because we cannot falsify a theory, does not mean we should give it any credence - we should treat the unknown as what it is - unknown. And because pretty much all human thought, reason, and action functions on the basis of evidence or simply past experience, something that is unknown and unknowable should in my opinion simply be classified as non-existent.
(Sorry for my poor argumentation, but when I say non-existent here, I don't mean it as a hard statement, but rather that we should prune the idea from our ontology - in the same way that we don't say that there "might or might not be invisible rubber-duckies in space" or that there "might or might not be a monolith on Europa" etc.)