I think I see where you're coming from with this, but your argument entirely elides the matter at hand by presupposing that 'consistent' definitions must non-controversially exist. The positive atheists' claim is simply that the general definition of deity cannot be 'consistent', but the negative atheist would approach a specific 'consistent' definition of a specific deity and argue that in point of fact that definition is not consistent. E.g., a theist claims that the divine circular square exists (either by handwaving its curved right angles entirely out of consideration, or making a special pleading claim regarding divine curves), and an atheist argues that, no, geometric figures with right angles cannot actual have perimeters uniformly equidistant from their center even if divine.
The sentence "a circular square does not exist" is not even vaguely meaningless in the face of someone asserting that, in fact, "a circular square exists". Reductio ad absurdum in formal logical terms is proof that a conclusion is false because it relies on a premise that leads to a contradiction. One of the premises put forth by a proponent of a deity's existence is by necessity the definition of that deity; it is a perfectly valid tactic on the part of a denier of that deity's existence to demonstrate a contradiction arises from that definition. Indeed, given that exhaustive proof of non-existence is impossible in this case, demonstrating a contradiction must arise from the premises arguing in favor of said deity's existence is the only feasible means to conclude the deity does not exist, assuming the asserter does not make falsifiable claims regarding the deity's interaction with the world (either historically or contemporaneously).
The question as to whether something logically contradictory exists or does not exist must make sense, or logic itself is going to break down. It is the phrase "circular square" that is meaningless, not "a circular square does not exist". The statement "something that cannot exist does not exist" may be banal, but it's hardly meaningless.