""atheists is at the very least a shared view that a deity or deities are unproven, unlikely, do not exist, should not exist for moral reasons, or some combination of those..."
No, atheism is a belief that no higher power exists, period. You mix agnosticism with atheism. There is no "should not" or "unlikely" in atheism,"
^Well, I was trying to be broad and non-divisive with my example, so "unlikely" I would agree is probably more befitting agnosticism rather than atheism, though I would contend that such an agnostic who views a deity as being not "unknowable" but rather outright states one is "unlikely" to exist would be close enough to that imaginary line between agnosticism and atheism to practically be straddling it.
As for "should not exist," again, trying to be inclusive rather than exclusive with my definition...
I'm taking the "should not exist" (or, rather, perhaps it would be better stated "would be better if one/because one did/does not exist,") as a very-abbreviated form of what Hitchens termed an "Anti-Theist" stance, one he shares (albeit from different argumentative angles) with Nietzsche, and one I myself share (as will likely be evidence by The Great Debate when that comes out.)
So, I agree, a couple of iffy ones there in terms of terminology, I just didn't want to tread on anyone's toes or personal take as to what they feel is or is not part of their own view of atheism...
Again, aside from that one rather obvious stance you have to take, I think it's rather open, and many of its authors and texts are very much take-it-or-leave-it in kind.