No need to expand. I'll stop you there. I see exactly where you're slipping up and it's not worth it to me to address or read the rest of your post when I see the fault so early.I don't assume you're a positive atheist, but I also don't assume you're a negative atheist. I'll expand on this below.
You're trying to split atheism like this:
The problem there is that you aren't even giving the larger circle a label. When I say I'm an atheist, I'm pointing at the larger circle, but you aren't allowing that to have an identity. You're trying to force people into sides, and that's not how it works.
This is a more accurate representation of how these categories work:
This allows for the larger category to have an identity. Any subcategories can be fitted into smaller circles within the larger one. Those smaller circles share the identity of the larger circle while having additional information of their own. The larger circle does not share that additional information of the smaller one.
If we give the big, blue circle the identity of 'A', then the smaller purple circle is 'A + B'.
In the case of atheism, the blue circle represents everything that any form of atheism shares. That only includes the lack of belief in a god or gods.
The smaller purple circle also includes that larger definition, but adds on an additional truth claim that there are no gods.
Additional circles can be added within the larger circle. They can even overlap with each other. They will always only remain a smaller part of the larger blue circle though.
This isn't just about how atheism works. This is about the basics of identities and how they relate to each other mathematically and categorically.
This is the one additional thing from the rest of your post I would like to address. Agnostic Atheism is a thing. It's even a label that describes me. Allow me to explain.(then you would run into problems such as agnosticism becoming a type of atheism as well, despite the historical insistence of agnostics not to be labeled as atheists even in the negative sense)
Gnosticism describes a position of certain knowledge. Therefore, agnosticism is a position of not claiming certain knowledge.
If theism is a belief in a god or gods, then atheism is it's opposite (without belief in a god or gods).
One directs your knowledge claims and the other directs your position on beliefs. You can combine these.
• An agnostic theist believes there is a god or gods, but does not claim certainty in them
• A gnostic theist believes there is a god or gods and claims certainty in them
In the second circle above, agnostic theism is the larger blue circle and gnostic theism is the smaller purple circle within it.
• An agnostic atheist does not hold a belief in a god or gods, but does not claim certainty about their nonexistence
• A gnostic atheist does not hold a belief in a god or gods and claims certainty in their nonexistence
In the second circle above, agnostic atheism is the larger blue circle and gnostic atheism is the smaller purple circle within it.