"the most simple definition of atheism is "without god."
And that's just etymology. Do you know that sinister also means left-handed? Does that mean the meaning "left-handed" is more correct? More simple? No, it means language has developed since the original meaning of the word was set...
"weak or strong, implicit or explicit... it's all atheism. "
You're trying to have, essentially, an academic discussion with colloquial terms. This is not a confusion of terminology, it's a misuse of it. Academic study of religion developed that language specifically to resolve the lack of...
"We do not accept or reject THE idea of god, we accept or reject OUR idea of god."
No. Regardless of how an atheist comes to develop, refine, or alter their idea of what a god is or is not, they will continue to not believe in it. What's more, they already don't believe in a deity they have...
If this sort of thing interests you, I'd recommend auditing a 100-level course in religious studies or at least finding the textbook recommendations for one and purchasing it. This is fundamental terminology in the study of religions and really irons out a lot of the confusing terms used...
"Categorizing the atheist experience is a bit like herding cats. Not all kneel at the altar of Dawkins."
You need not fall into Dawkins' cult of personality in order to be an Atheist. And I don't say that as a slur. I rather like Dawkins despite me being a Pagan.
"My beliefs are implicitly atheistic, in that I do not actively believe in any god concepts"
That's non-theism; the lack of belief, specifically, in a deity or deities. It's a wholly different category from atheism. Atheism, by necessity, is also non-theist. But there are a variety of faiths...
An atheist is not an atheist because they are not Christian or not Bhuddist or not Asatruar any more than a dog is not a cat because it's not a cheetah or not a lion or not a house cat. It is defined by its dog-ness not by it's lack of cat-ness.
Atheism is an active disbelief in metaphysical...