Thank you, but I'm happy just to hear you say whatever you wish to say on the matter. You have the right to choose your beliefs, as we all do.You are welcome to pull my definition apart.
However, on grounds of reason, I would think Eliminativism has to be eliminated. For it is simply not true to say that all people believe in God without evidence. Many -- whether rightly or wrongly, we can leave that undecided for now -- clearly sincerely believe they are possessed of evidence indicating the existence of a Creator. So the Eliminativism would have to be asserting that they simply have no such evidence at all; and that seems too easy for them to falsify.
And as for the second point, I suppose it is dependent on whether a scientific theory is supposed to genuinely reflect reality or to render the natural world serviceable to humans. If the latter, then the God Hypothesis would only be as "scientific" as it was useful in subduing the world to human hands: and that seems narrow. If, on the other hand, the purpose of science is to reflect how things really are, and if science is unable to reflect God, then the fault might well be on the limitations inherent in human science.
Either way, I don't think your Atheists have achieved any certainty through either position. They can only "rule out" God by being arbitrary, in both the Eliminativist and the Scientific Realist cases.