I'd not like to frame it that way, Recovery. I don't see myself as "refuting" the accuracy of "the Bible". A historian who critically examines what Berossus or Herodotus wrote does not aim to "refute" those ancient writers but rather assesses not just their accuracy but also their methods of composition, artfulness, ideological motives, and cultural context. There will be things that in objective examination will not be accurate, which might be invented or slanted, but that doesn't mean the book is itself refuted and can be dispensed with as an ancient source. All sources are slanted, inaccurate, etc. Ancient writers were not historians in the modern sense and they wrote from their own cultural point of view. Myth, folklore, and history were not carefully distinguished and narratives became better, more interesting stories through storytelling. A writer has the traditions at their disposal (which themselves draw on years of oral storytelling) and then crafts them in his or her own way in writing. I think the problem rather arises when as a religious text one demands that the stories are literally, unimpeachably true. Then the kind of normal literary examination of the text that one might do in the case of the Iliad or the Mahabharata becomes viewed as "attacking" or "trying to refute" the text. Rather, what is refuted in this instance, is the interpretation of the Flood myth that the Society (and YECs) proposes that makes historically and scientifically falsifiable claims. Then, yes, one could refute that. But the myth itself is ... a myth. I don't think it is without historical basis either. If you trace the history of the storytelling of this particular myth, from biblical to the Akkadian to the original Sumerian story, one could see that indeed the story likely preserves a memory of certain major floods that occurred in Mesopotamia in the Ubaid and Early Dynastic periods. But those memories have merged with certain folkloric archetypes that are not historical. But to take that ancient story, which was rooted in a very different cosmological and historical understanding of the world than we have now, and to take it as the basis for believing that it accurately relates a global flooding disaster in the recent past (bearing upon the scientific facts of the world as we currently understand them) is to stretch the story farther than it was intended to go.
I have written a lot on the Bible and looking at it from a critical perspective, including matters pertaining to historical accuracy. For instance, I consider the book of Jonah as a satirical story with certain social aims (in other words, it's akin to a parable). It's actually very funny satire; it would totally miss the point of the story to insist on it as literal history.