But if all mathematically possible universes exist anyway (or if they have a chance of existing), then the hypothetical "Azkaban from a universe without EY's logical inconsistencies" exists, no matter whether he writes about it or not. I don't see how writing about it could affect how real/not-real it is.

So by my understanding of how Eliezer explained it, he's not creating Azkaban, in the sense that writing about it causes it to exist, he's describing it. (This is not to say that he's not creating the fiction, but the way I see it create is being used in two different ways.) Unless I'm missing some mechanism by which imagining something causes it to exist, but that seems very unlikely.