If the object required for a negative existential claim is not the object in question, then we have created a new, second object with a property of non-existence.
No. If our claim is correct,
there never was any first object to begin with. Which was precisely what our claim
meant; if I claim that the King of France doesn't exist, I am saying that
there is no object corresponding to "the King of France".
And worse, as I've been trying to hammer home, we are not ascribing any object with the property of non-existence when we say it doesn't exist;
that is contradictory... if
there is an object, that means that object exists- so clearly we cannot say that there exists an object that doesn't exist. And besides being plainly contradictory, the view of language you're endorsing here is just woefully incomplete and untenable; words don't just pick out objects. They do far more than that. And we can talk coherently about non-referring phrases- that is, words that don't pick out any object. Nor do we need to
create objects in the case of non-referring phrases, as mere logical fictions, in order to satisfy a naive theory of meaning- especially not when doing so riddles us with contradiction and ontological paradox. There are no non-existent existents- and good riddance.
So once again,
negative existential claims are not first-order claims!